A. Krasnitz

We tested the hypothesis that de novo copy number variation (CNV) is associated with autism spectrum disorders (ASDs). We performed comparative genomic hybridization (CGH) on the genomic DNA of patients and unaffected subjects to detect copy number variants not present in their respective parents. Candidate genomic regions were validated by higher-resolution CGH, paternity testing, cytogenetics, fluorescence in situ hybridization, and microsatellite genotyping. Confirmed de novo CNVs were significantly associated with autism (P = 0.0005). Such CNVs were identified in 12 out of 118 (10%) of patients with sporadic autism, in 2 out of 77 (3%) of patients with an affected first-degree relative, and in 2 out of 196 (1%) of controls. Most de novo CNVs were smaller than microscopic resolution. Affected genomic regions were highly heterogeneous and included mutations of single genes. These findings establish de novo germline mutation as a more significant risk factor for ASD than previously recognized.

Genomic analysis provides insights into the role of copy number variation in disease, but most methods are not designed to resolve mixed populations of cells. In tumours, where genetic heterogeneity is common, very important information may be lost that would be useful for reconstructing evolutionary history. Here we show that with flow-sorted nuclei, whole genome amplification and next generation sequencing we can accurately quantify genomic copy number within an individual nucleus. We apply single-nucleus sequencing to investigate tumour population structure and evolution in two human breast cancer cases. Analysis of 100 single cells from a polygenomic tumour revealed three distinct clonal subpopulations that probably represent sequential clonal expansions. Additional analysis of 100 single cells from a monogenomic primary tumour and its liver metastasis indicated that a single clonal expansion formed the primary tumour and seeded the metastasis. In both primary tumours, we also identified an unexpectedly abundant subpopulation of genetically diverse 'pseudodiploid' cells that do not travel to the metastatic site. In contrast to gradual models of tumour progression, our data indicate that tumours grow by punctuated clonal expansions with few persistent intermediates.

<h2>Summary</h2> Cancer progression involves the gradual loss of a differentiated phenotype and acquisition of progenitor and stem-cell-like features. Here, we provide novel stemness indices for assessing the degree of oncogenic dedifferentiation. We used an innovative one-class logistic regression (OCLR) machine-learning algorithm to extract transcriptomic and epigenetic feature sets derived from non-transformed pluripotent stem cells and their differentiated progeny. Using OCLR, we were able to identify previously undiscovered biological mechanisms associated with the dedifferentiated oncogenic state. Analyses of the tumor microenvironment revealed unanticipated correlation of cancer stemness with immune checkpoint expression and infiltrating immune cells. We found that the dedifferentiated oncogenic phenotype was generally most prominent in metastatic tumors. Application of our stemness indices to single-cell data revealed patterns of intra-tumor molecular heterogeneity. Finally, the indices allowed for the identification of novel targets and possible targeted therapies aimed at tumor differentiation. <h3>Video Abstract</h3>

Although p53 inactivation promotes genomic instability1 and presents a route to malignancy for more than half of all human cancers2,3, the patterns through which heterogenous TP53 (encoding human p53) mutant genomes emerge and influence tumorigenesis remain poorly understood. Here, in a mouse model of pancreatic ductal adenocarcinoma that reports sporadic p53 loss of heterozygosity before cancer onset, we find that malignant properties enabled by p53 inactivation are acquired through a predictable pattern of genome evolution. Single-cell sequencing and in situ genotyping of cells from the point of p53 inactivation through progression to frank cancer reveal that this deterministic behaviour involves four sequential phases-Trp53 (encoding mouse p53) loss of heterozygosity, accumulation of deletions, genome doubling, and the emergence of gains and amplifications-each associated with specific histological stages across the premalignant and malignant spectrum. Despite rampant heterogeneity, the deletion events that follow p53 inactivation target functionally relevant pathways that can shape genomic evolution and remain fixed as homogenous events in diverse malignant populations. Thus, loss of p53-the 'guardian of the genome'-is not merely a gateway to genetic chaos but, rather, can enable deterministic patterns of genome evolution that may point to new strategies for the treatment of TP53-mutant tumours.

In very-high-energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, (dE/L2)/deta, is equal to f(g(2)&mgr;L) (g(2)&mgr;)(3)/g(2), where &mgr;(2) is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, a nonperturbative computation of f(g(2)&mgr;L) shows that it varies rapidly for small g(2)&mgr;L but varies only by approximately 25%, from 0.208+/-0.004 to 0.257+/-0. 005, for a wide range 35.36- 296.98 in g(2)&mgr;L. This includes the range relevant for collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Extrapolating to SU(3), we estimate dE/deta for Au-Au collisions in the central region at RHIC and LHC.

At very high energies, in the infinite momentum frame and in light-cone gauge, a hard scale proportional to the high parton density arises in QCD. In an effective theory of QCD at small x, this scale is of order αsμ, where μ is simply related to the gluon density at higher rapidities. The ab initio real time evolution of small x modes in a nuclear collision can be described consistently in the classical effective theory and various features of interest can be studied non-perturbatively. In this paper, we discuss results from a real time SU(2) lattice computation of the production of gluon jets at very high energies. At very large transverse momenta, kt ⩾ μ, our results match the predictions from pQCD based mini-jet calculations. Novel non-perturbative behavior of the small x modes is seen at smaller momenta kt ∼ αsμ. Gauge invariant energy-energy correlators are used to estimate energy distributions evolving in proper time.

The early stages of a relativistic heavy-ion collision are examined in the framework of an effective classical SU(3) Yang-Mills theory in the transverse plane. We compute the initial energy and number distributions, per unit rapidity, at midrapidity, of gluons produced in high-energy heavy-ion collisions. We discuss the phenomenological implications of our results in light of the recent Relativistic Heavy-Ion Collider data.

We used high-resolution array analysis to discover a recurrent lung cancer amplicon located at 14q13.3. Low-level gain of this region was detected in 15% of lung cancer samples, and high-level amplification was detected in an additional 4% of samples. High-level focal amplification appears to be specific to lung cancers, because it was not detected in >500 samples of other tumor types. Mapping of the commonly amplified region revealed there are three genes in the core region, all of which encode transcription factors with either established lung developmental function (TTF1/NKX2-1, NKX2-8) or potential lung developmental function (PAX9). All three genes were overexpressed to varying degrees in amplified samples, although TTF1/NKX2-1 was not expressed in the squamous cancer subtype, consistent with previous reports. Remarkably, overexpression of any pairwise combination of these genes showed pronounced synergy in promoting the proliferation of immortalized human lung epithelial cells. Analysis of human lung cancer cell lines by both RNAi and ectopic overexpression further substantiates an oncogenic role for these transcription factors. These results, taken together with previous reports of oncogenic alterations of transcription factors involved in lung development (p63, CEBPA), suggest genetic alterations that directly interfere with transcriptional networks normally regulating lung development may be a more common feature of lung cancer than previously realized.

The initial gluon multiplicity per unit area per unit rapidity, $\mathrm{dN}/{L}^{2}/d\ensuremath{\eta}$, in high energy nuclear collisions, is equal to ${f}_{N}({g}^{2}\ensuremath{\mu}L)({g}^{2}\ensuremath{\mu}{)}^{2}/{g}^{2}$, with ${\ensuremath{\mu}}^{2}$ proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute ${f}_{N}({g}^{2}\ensuremath{\mu}L)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.14\ifmmode\pm\else\textpm\fi{}0.01$ for a wide range in ${g}^{2}\ensuremath{\mu}L$. Extrapolating to SU(3), we predict $\mathrm{dN}/{L}^{2}/d\ensuremath{\eta}$ for values of ${g}^{2}\ensuremath{\mu}L$ relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, $\mathrm{dN}/{L}^{2}/{d}^{2}{k}_{\ensuremath{\perp}}$, and show it to be well behaved at low ${k}_{\ensuremath{\perp}}$.

We comment on the relation of our previous work on the classical gluodynamics of high energy nuclear collisions to recent work by Lappi [Phys. Rev. C 67 (2003) 054903]. While our results for the non-perturbative number liberation coefficient agree, those for the energy disagree by a factor of 2. This discrepancy can be traced to an overall normalization error in our non-perturbative formula for the energy. When corrected for, all previous results are in excellent agreement with those of Lappi. The implications of the results of these two independent computations for RHIC phenomenology are noted.

We extend previous work on high energy nuclear collisions in the Color Glass Condensate model to study collisions of finite ultrarelativistic nuclei. The changes implemented include a) imposition of color neutrality at the nucleon level and b) realistic nuclear matter distributions of finite nuclei. The saturation scale characterizing the fields of color charge is explicitly position dependent, $\Lambda_s=\Lambda_s(x_T)$. We compute gluon distributions both before and after the collisions. The gluon distribution in the nuclear wavefunction before the collision is significantly suppressed below the saturation scale when compared to the simple McLerran-Venugopalan model prediction, while the behavior at large momentum $p_T\gg \Lambda_s$ remains unchanged. We study the centrality dependence of produced gluons and compare it to the centrality dependence of charged hadrons exhibited by the RHIC data. We demonstrate the geometrical scaling property of the initial gluon transverse momentum distributions for different centralities. Classical Yang-Mills results for $p_T < \Lambda_s$ are simply matched to perturbative QCD computations for $p_T > \Lambda_s$-the resulting energy per particle is significantly lower than the purely classical estimates. Our results for nuclear collisions can be used as initial conditions for quantitative studies of the further evolution and possible equilibration of hot and dense gluonic matter produced in heavy ion collisions. Finally, we study $pA$ collisions within the classical framework. Our results agree well with previously derived analytical results in the appropriate kinematical regions.

We compute numerically the topological charge distribution in the initial stage of a high energy heavy ion collision. This charge distribution is generated by Chern-Simons number fluctuations associated with the dynamics of strong classical fields in the initial state. The distribution is found to be quite narrow at RHIC and LHC energies reflecting a small value of the topological susceptibility. Thus the effective potential of classical fields is shallow in the $\theta$-direction likely creating favorable conditions for the subsequent generation of P-odd bubbles.

Abstract We examined copy number changes in the genomes of B cells from 58 patients with chronic lymphocytic leukemia (CLL) by using representational oligonucleotide microarray analysis (ROMA), a form of comparative genomic hybridization (CGH), at a resolution exceeding previously published studies. We observed at least 1 genomic lesion in each CLL sample and considerable variation in the number of abnormalities from case to case. Virtually all abnormalities previously reported also were observed here, most of which were indeed highly recurrent. We observed the boundaries of known events with greater clarity and identified previously undescribed lesions, some of which were recurrent. We profiled the genomes of CLL cells separated by the surface marker CD38 and found evidence of distinct subclones of CLL within the same patient. We discuss the potential applications of high-resolution CGH analysis in a clinical setting.

Copy number alterations (CNAs) play an important role in molding the genomes of breast cancers and have been shown to be clinically useful for prognostic and therapeutic purposes. However, our knowledge of intra-tumoral genetic heterogeneity of this important class of somatic alterations is limited. Here, using single-cell sequencing, we comprehensively map out the facets of copy number alteration heterogeneity in a cohort of breast cancer tumors. Ou/var/www/html/elife/12-05-2020/backup/r analyses reveal: genetic heterogeneity of non-tumor cells (i.e. stroma) within the tumor mass; the extent to which copy number heterogeneity impacts breast cancer genomes and the importance of both the genomic location and dosage of sub-clonal events; the pervasive nature of genetic heterogeneity of chromosomal amplifications; and the association of copy number heterogeneity with clinical and biological parameters such as polyploidy and estrogen receptor negative status. Our data highlight the power of single-cell genomics in dissecting, in its many forms, intra-tumoral genetic heterogeneity of CNAs, the magnitude with which CNA heterogeneity affects the genomes of breast cancers, and the potential importance of CNA heterogeneity in phenomena such as therapeutic resistance and disease relapse.

Results of a large scale numerical simulation show that the high temperature Chern-Simons number diffusion rate in the electroweak theory has a classical limit Γ = κ(αwT)4,where κ = 1.09 ± 0.04 and αw is the weak fine structure constant.

Orienting cancer drug discovery to the patient requires relating the genetic features of tumors to acquired gene and pathway dependencies and identifying small-molecule therapeutics that target them.

We use numerical simulations to study the spatial structure of a quark and an antiquark in the imaginary-time excitations which mediate the Debye screening of color singlet sources in the high-temperature phase of QCD. We find that these correlation functions are very similar to the zero-temperature wave functions of the corresponding particles. This result contrasts with results on the \ensuremath{\rho} and nucleon screening lengths for these sources, which are well described by a gas of free or weakly interacting quarks.

One of the key questions about genomic alterations in cancer is whether they are functional in the sense of contributing to the selective advantage of tumor cells. The frequency with which an alteration occurs might reflect its ability to increase cancer cell growth, or alternatively, enhanced instability of a locus may increase the frequency with which it is found to be aberrant in tumors, regardless of oncogenic impact. Here we've addressed this on a genome-wide scale for cancer-associated focal deletions, which are known to pinpoint both tumor suppressor genes (tumor suppressors) and unstable loci. Based on DNA copy number analysis of over one-thousand human cancers representing ten different tumor types, we observed five loci with focal deletion frequencies above 5%, including the A2BP1 gene at 16p13.3 and the MACROD2 gene at 20p12.1. However, neither RNA expression nor functional studies support a tumor suppressor role for either gene. Further analyses suggest instead that these are sites of increased genomic instability and that they resemble common fragile sites (CFS). Genome-wide analysis revealed properties of CFS-like recurrent deletions that distinguish them from deletions affecting tumor suppressor genes, including their isolation at specific loci away from other genomic deletion sites, a considerably smaller deletion size, and dispersal throughout the affected locus rather than assembly at a common site of overlap. Additionally, CFS-like deletions have less impact on gene expression and are enriched in cell lines compared to primary tumors. We show that loci affected by CFS-like deletions are often distinct from known common fragile sites. Indeed, we find that each tumor tissue type has its own spectrum of CFS-like deletions, and that colon cancers have many more CFS-like deletions than other tumor types. We present simple rules that can pinpoint focal deletions that are not CFS-like and more likely to affect functional tumor suppressors.

We compute the elliptic flow generated by classical gluon fields in a high energy nuclear collision. The classical gluon fields are described by a typical momentum scale, the saturation scale Λs, which is, for RHIC energies, of the order of 1–2 GeV. A significant elliptic flow is generated only over time scales on the order of the system size R. The flow is dominated by soft modes pT∼Λs/4 which linearize at very late times τ∼R⪢1/Λs. We discuss the implications of our result for the theoretical interpretation of the RHIC data.

We have carried out a simulation of QCD using the hybrid-molecular-dynamics algorithm with two flavors of staggered quarks. The spectrum was calculated for $\frac{6}{{g}^{2}=5.6}$ and dynamical quark masses ${\mathrm{am}}_{q}=0.025 \mathrm{and} 0.01$. Lattice sizes of ${12}^{4}$, ${12}^{3}$\ifmmode\times\else\texttimes\fi{}24, and ${16}^{4}$ were used to generate the gauge configurations. Hadron propagators were calculated with both staggered and Wilson quarks on doubled or quadrupled latices. Finite-size effects are visible on the smaller lattices. Some improvement in the $\ensuremath{\rho}$-to-nucleon mass ratio and chiral symmetry is seen as compared to previous calculations, but, as in most lattice calculations, the proton-to-$\ensuremath{\rho}$ mass ratio remains larger than in the real world and the proton-$\ensuremath{\Delta}$ splitting is too small.

Copy-number variants such as germ-line deletions and amplifications are associated with inherited genetic disorders including familial cancer. The gene or genes responsible for the majority of familial clustering of pancreatic cancer have not been identified. We used representational oligonucleotide microarray analysis (ROMA) to characterize germ-line copy number variants in 60 cancer patients from 57 familial pancreatic cancer kindreds. Fifty-seven of the 60 patients had pancreatic cancer and three had non-pancreatic cancers (breast, ovary, ovary). A familial pancreatic cancer kindred was defined as a kindred in which at least two first-degree relatives have been diagnosed with pancreatic cancer. Copy-number variants identified in 607 individuals without pancreatic cancer were excluded from further analysis. A total of 56 unique genomic regions with copy-number variants not present in controls were identified, including 31 amplifications and 25 deletions. Two deleted regions were observed in two different patients, and one in three patients. The germ-line amplifications had a mean size of 662Kb, a median size of 379Kb (range 8.2Kb to 2.5Mb) and included 425 known genes. Examples of genes included in the germ-line amplifications include the MAFK, JunD and BIRC6 genes. The germ-line deletions had a mean size of 375Kb, a median size 151Kb (range 0.4Kb to 2.3Mb) and included 81 known genes. In multivariate analysis controlling for region size, deletions were 90% less likely to involve a gene than were duplications (p

Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac operator are made on ensembles of equilibrium gauge field configurations in quenched SU(3) lattice gauge theory. The results are compared with exact analytical predictions in the microscopic finite-volume scaling regime.

We discuss the confining and chiral-symmetry breaking properties of QCD with a large number of flavors Nf. In a Monte Carlo simulation of QCD with Nf = 16 staggered fermions, we find clear evidence of a first order bulk phase transition which separates phases with broken and unbroken chiral symmetry. This is consistent with extrapolations of earlier studies with smaller Nf, and is also as expected from general arguments. Thus, even when the perturbative renormalization group flow has a new infrared stable fixed point near the origin, lattice artifacts induce chiral symmetry breaking, and presumably confinement, at sufficiently strong coupling.

The first results of numerical simulations of quantum chromodynamics on the Intel iPSC/860 parallel processor are presented. We performed calculations with two flavors of Kogut-Susskind quarks at ${N}_{t}=6$ with masses of $0.15T$ and $0.075T$ (0.025 and 0.0125 in lattice units) in order to locate the crossover from the low-temperature regime of ordinary hadronic matter to the high-temperature chirally symmetric regime. As with other recent two-flavor simulations, these calculations are insufficient to distinguish between a rapid crossover and a true phase transition. The phase transition is either absent or feeble at this quark mass. An improved estimate of the crossover temperature in physical units is given and results are presented for the hadronic screening lengths in both the high- and low-temperature regimes.

We determine the sphaleron transition rate using real time lattice simulations of the classical system. An improved definition of the lattice topological charge allows us to obtain a more reliable estimate of the transition rate. For an SU(2) Yang-Mills-Higgs system in the broken phase we find the transition rate to be strongly suppressed, and we have observed no sphaleron transitions in the range of coupling constants used. For a pure SU(2) Yang-Mills system in large volumes the rate behaves as $\kappa (\alpha_w T)^4$, with $\kappa$ slightly decreasing as the lattice spacing is reduced. If the lattice size is reduced to about twice the magnetic screening length, the rate is suppressed by finite-size effects, and $\kappa$ is approximately proportional to the lattice spacing. Our rate measurements are supplemented by analysis of gauge field correlation functions in the Coulomb gauge.

We have carried out a numerical study of the high-temperature behavior of lattice QCD with two flavors of staggered quarks. Our simulations were performed on ${16}^{3}$\ifmmode\times\else\texttimes\fi{}8 lattices with a quark mass ${m}_{q}=0.0125$, in units of the inverse lattice spacing. By monitoring the Wilson-Polyakov line, the chiral order parameter $〈\overline{\ensuremath{\psi}}\ensuremath{\psi}〉$, and the average plaquette, we have determined that a crossover between the low-temperature state of ordinary hadronic matter and the high-temperature quark-gluon plasma occurs at a gauge coupling of $\frac{6}{{g}^{2}}=5.54(2)$. Thermodynamic quantities do not show a large jump, although the equilibration time becomes quite long in the vicinity of the crossover. We have measured the entropy densities in the neighborhood of the crossover and further into the plasma phase. Measurements of the hadronic screening lengths and the Debye screening lengths were made which cast light on the differences between the two regimes. Finally, we measured the topological susceptibilities to further explore the chiral properties of QCD.

Numerical simulations of interacting quarks and glu ons may be the best way to calculate the structure of protons and neutrons, as well as the nature of the very early universe or the interiors of neutron stars. Such simulations are limited by the availability of computer power. We are carrying out a program of simulations on multiple instruction, multiple data (MIMD) parallel computers. We describe here the goals of this project, discuss the way in which the computations are adapted to parallel computers and the performance they achieve, and present a few preliminary results.

The exact renormalization group and a manifestly gauge invariant version, T.R. Morris flow equations for phase transitions in statistical physics and QCD, D-U. Jungnickel and C. Wetterich realization of symmetries and the c-theorem, S. Forte and J.I. Latorre the density matrix renormalization group, quantum groups and conformal field theory, G. Sierra and M.A. Martin-Delgado Wilsonian effective action with an auxiliary field for the field strength, U. Ellwanger supersymmetric gauge theories in the exact renormalization group approach, F. Vian Polchinski ERG equation and 2D scalar field theory, Y. Kubyshin et al on gauge invariant Wilsonian flows, D.F. Litim and J.M. Pawlowski non-perturbative analysis of chiral critical behaviour in QED, J-I. Sumi non-pertubative renormalization group and quantum tunnelling, A. Horikoshi the modular and renormalization groups in the quantum hall effect, B.P. Dolan two-loop QCD vertices, WST identities and RG quantities, A.I. Davydychev et al.

We study hadron thermodynamics with Wilson quarks. The crossover curve between the high-and low-temperature phases is determined as a function of gauge coupling and hopping parameter on ${8}^{3}$\ifmmode\times\else\texttimes\fi{}4 lattices. Screening lengths are calculated in the vicinity of the crossover region, and meson masses are calculated along the crossover curve on ${8}^{2}$\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}4 and ${8}^{3}$\ifmmode\times\else\texttimes\fi{}16 lattices, respectively.

We have carried out a simulation of quantum chromodynamics using the hybrid-molecular-dynamics algorithm with two flavors of Kogut-Susskind quarks. We have used Kogut-Susskind and Wilson valence quarks to calculate the hadron mass spectrum. Among our extensive results we discuss baryon hyperfine splitting, the nucleon-to-\ensuremath{\rho} mass ratio, the sclar-to-tensor-glueball mass ratio, and the quantization and susceptibility of the topological charge. We have used a gauge coupling of 6/${\mathit{g}}^{2}$=5.60, and quark masses ${\mathit{am}}_{\mathit{q}}$=0.025 and 0.01, in generating gauge configurations on ${12}^{4}$, ${12}^{3}$\ifmmode\times\else\texttimes\fi{}24, and ${16}^{4}$ lattices.

Three-dimensional lattice QCD is studied by Monte Carlo simulations within the quenched approximation. At zero temperature a quark-antiquark condensate is observed in the limit of vanishing quark masses. The condensate vanishes continuously at the finite-temperature deconfinement phase transition of the theory. A natural interpretation of this phenomenon in the full theory with dynamical quarks is in terms of the spontaneous flavor symmetry breaking U(Nf)→U(Nf/2)×U(Nf/2). In addition, the spectrum of low-lying Dirac operator eigenvalues is computed and found to be consistent with a flat distribution at zero temperature, in agreement with analytical predictions.

We have carried out spectrum calculations with two flavors of dynamical Kogut-Susskind quarks on four lattice sizes from ${8}^{3}$\ifmmode\times\else\texttimes\fi{}24 to ${16}^{3}$\ifmmode\times\else\texttimes\fi{}24 at couplings that correspond to chiral symmetry restoration for a lattice with six time slices. We estimate that the linear spatial sizes of the lattices range from 1.8 to 3.6 fm. We find significant finite-size effects for all particles between the smallest and largest volume with the larger quark mass that we study, $a{m}_{q}=0.025$, where $a$ is the lattice spacing. The nucelon experiences the largest effect of about 6%. We also study a lighter quark mass, $a{m}_{q}=0.0125$, on the two largest lattices. Effects of the dynamical and valence quark masses on the hadron spectrum are studied both directly, by comparing the two simulations, and by extracting mass derivatives from the correlation functions. We do not find much improvement in the nucleon to $\ensuremath{\rho}$ mass ratio as we decrease the quark mass at this lattice spacing. Finally, we report on an unsuccessful attempt to see effects of the $\ensuremath{\rho}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay on the $\ensuremath{\rho}$ mass, and on studies of Wilson and Kogut-Susskind hadron masses with large valence quark masses.

We present an analysis of hadronic spectroscopy for Wilson valence quarks with dynamical staggered fermions at a lattice coupling $\frac{6}{{g}^{2}}=5.6$ at a sea-quark mass of ${\mathrm{am}}_{q}=0.01 \mathrm{and} 0.025$, and of Wilson valence quarks in the quenched approximation at $\ensuremath{\beta}=5.85 \mathrm{and} 5.95$, both on ${16}^{3}$ \ifmmode\times\else\texttimes\fi{} 32 lattices. We make comparisons with our previous results with dynamical staggered fermions at the same parameter values but on ${16}^{4}$ lattices doubled in the temporal direction.

We obtain estimates of the lightest glueball masses, the string tension, and the topological susceptibility in an exploratory study of QCD with two light flavors of quarks. Our calculations are performed at $\ensuremath{\beta}=5.6$ with staggered quark masses ${m}_{q}=0.010 \mathrm{and} 0.025$ and on lattices ranging from ${12}^{4}$ to ${16}^{4}$. Our estimates suggest that, just as in the pure gauge theory, the ${0}^{++}$ is the lightest glueball with the ${2}^{++}$ about 50% heavier. Our ${m}_{q}=0.01$ results predict a ${0}^{++}$ glueball mass of about 1.6 times the $\ensuremath{\rho}$ mass and the square root of the string tension of about 0.48 times the $\ensuremath{\rho}$ mass, which is surprisingly close to the usual phenomenologically motivated estimates of around 0.55. Our value of the topological susceptibility at ${m}_{q}=0.01$ is consistent with the prediction, to $O({m}_{q})$ of the standard anomalous Ward identity. However, the variation of this susceptibility between ${m}_{q}=0.01$ and ${m}_{q}=0.025$ is weaker than the linear dependence one expects at small ${m}_{q}$ in the broken-chiral-symmetry phase of QCD.

We show the use of 5'-Acrydite oligonucleotides to copolymerize single-cell DNA or RNA into balls of acrylamide gel (BAGs). Combining this step with split-and-pool techniques for creating barcodes yields a method with advantages in cost and scalability, depth of coverage, ease of operation, minimal cross-contamination, and efficient use of samples. We perform DNA copy number profiling on mixtures of cell lines, nuclei from frozen prostate tumors, and biopsy washes. As applied to RNA, the method has high capture efficiency of transcripts and sufficient consistency to clearly distinguish the expression patterns of cell lines and individual nuclei from neurons dissected from the mouse brain. By using varietal tags (UMIs) to achieve sequence error correction, we show extremely low levels of cross-contamination by tracking source-specific SNVs. The method is readily modifiable, and we will discuss its adaptability and diverse applications.

We present results of a lattice simulation of quantum chromodynamics with two degenerate flavors of dynamic Wilson fermions at $\frac{6}{{g}^{2}}=5.3$ at each of two dynamical fermion hopping parameters $\ensuremath{\kappa}=0.1670 \mathrm{and} 0.1675$ corresponding to pion masses in lattice units of about 0.45 and 0.31. The simulations include three other values of valence quark mass, in addition to the dynamical quarks. We present calculations of masses and of the decay constants of vector mesons and of pseudoscalars, including the $D$-meson decay constant. The effects of sea quarks on matrix elements and spectroscopy are small.

We have measured some simple matrix elements for pseudoscalar and vector mesons made of Wilson valance quarks and staggered sea quarks at $\ensuremath{\beta}=5.6$ at sea quark masses $a{m}_{q}=0.01 \mathrm{and} 0.025$. Our measurements include the decay constants of pseudoscalars (including ${f}_{D}$), the wave function at the origin (or decay constant) of vector mesons, and the calculation of quark masses from current algebra. The effects of sea quarks on the simulations are small. We make comparisons to quenched simulations at similar values of the lattice spacing ($\frac{1}{a}\ensuremath{\simeq}2$ GeV).

We report on a study of hadron thermodynamics with two flavors of Wilson quarks on 12^3x6 lattices. We have studied the crossover between the high and low temperature regimes for three values of the hopping parameter, kappa=0.16, 0.17, and 0.18. At each of these values of kappa we have carried out spectrum calculations on 12^3x24 lattices for two values of the gauge coupling in the vicinity of the crossover in order to set an energy scale for our thermodynamics calculations and to determine the critical value of the gauge coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we find coexistence between the high and low temperature regimes over 1,000 simulation time units indicating either that the equilibration time is extremely long or that there is a possibility of a first order phase transition. The pion mass is large at the crossover values of the gauge coupling, but the crossover curve has moved closer to the critical curve along which the pion and quark masses vanish, than it was on lattices with four time slices. In addition, values of the dimensionless quantity T_c/m_rho are in closer agreement with those for staggered quarks than was the case at N_t=4. (A POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)

At very high energies, the high parton densities (characterized by a semi-hard saturation scale \Lambda_s) ensure that parton distributions can be described by a classical effective field theory with remarkable properties analogous to those of spin glass systems. This color glass condensate (CGC) of gluons also provides the initial conditions for multi-particle production in high energy nuclear collisions. In this talk, we briefly summarize recent theoretical and phenomenological progress in the CGC approach to small x physics. In particular, we discuss recent numerical work on the real time gluodynamics of partons after a nuclear collision. The implications of this work for the theoretical study of thermalization in nuclear collisions and on the phenomenological interpretation of results of the recent RHIC experiments are also discussed.

We have extended our previous study of the lattice QCD spectrum with 2 flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the $\Delta$ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that $m_\pi^2 \propto m_q$, and $f_\pi$ is estimated. Use of undoubled lattices removes problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of $am_q=0.01$ when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, $am_q=0.025$. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.

Abstract Measuring minimal residual disease in cancer has applications for prognosis, monitoring treatment and detection of recurrence. Simple sequence-based methods to detect nucleotide substitution variants have error rates (about 10−3) that limit sensitive detection. We developed and characterized the performance of MASQ (multiplex accurate sensitive quantitation), a method with an error rate below 10−6. MASQ counts variant templates accurately in the presence of millions of host genomes by using tags to identify each template and demanding consensus over multiple reads. Since the MASQ protocol multiplexes 50 target loci, we can both integrate signal from multiple variants and capture subclonal response to treatment. Compared to existing methods for variant detection, MASQ achieves an excellent combination of sensitivity, specificity and yield. We tested MASQ in a pilot study in acute myeloid leukemia (AML) patients who entered complete remission. We detect leukemic variants in the blood and bone marrow samples of all five patients, after induction therapy, at levels ranging from 10−2 to nearly 10−6. We observe evidence of sub-clonal structure and find higher target variant frequencies in patients who go on to relapse, demonstrating the potential for MASQ to quantify residual disease in AML.

We discuss some aspects of the hadron spectrum with two flavors of Kogut-Susskind dynamical quarks at 6/g2 = 5.6 and amq = 0.01 and 0.025, using both Kogut-Susskind and Wilson valence quarks. Our high statistics simulations allow us to study systematic errors. Among the problematic features of our results are a dip in the pion effective mass which we ascribe to replicating the lattice in the time direction and large finite size effects in the baryon masses. We also compare the full QCD results to a quenched simulation at similar lattice spacing and quark masses to test whether the effects of dynamical fermions can be absorbed into renormalization of the lattice parameters.

At very high energies, the partons in the nuclear wavefunction form a color glass condensate.Since the occupation number of partons in the color glass condensate is large, classical methods can be used to compute multi-particle production in the initial instants of a high energy heavy ion collision.Non-perturbative expressions are derived relating the distributions of produced partons to those of wee partons in the wavefunctions of the colliding nuclei.The time evolution of components of the stress-energy tensor is studied and the impact parameter dependence of elliptic flow is extracted.We discuss the space-time picture that emerges and interpret the RHIC data within this framework.

As part of an ongoing effort to characterize the high temperature phase of QCD, in a numerical simulation using the staggered fermion scheme, we measure the quark baryon density in the vicinity of a fixed test quark at high temperature and compare it with similar measurements at low temperature and at the crossover temperature. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at T=0.75 ${\mathit{T}}_{\mathit{c}}$ the total induced quark number shows a surprisingly large component attributable to baryonic screening. A companion simulation of a simple flux tube model produces similar results and also suggests a plausible phenomenological scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.

We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-time dynamics of non-abelian gauge theories at high temperature. We see no sign of the predicted behavior. This indicates that perturbative concepts like color conductivity and Landau damping might be irrelevant at temperatures corresponding to the electroweak scale.

A simple quantum-mechanical example is used to analyze the effect of field configuration copying on a fermion correlation function. It is shown that the copying procedure may result in a large correction to the fermion effective mass except for short-time correlations in the low-temperature regime. This correction possibly explains the oscillatory behavior of meson effective masses in a recent lattice QCD calculation.

The HTMCGC collaboration has been simulating lattice QCD with two light staggered quarks with masses mq = 0.0125 and also mq = 0.00625 on a 163 × 8 lattice. We have been studying the behaviour of the transition from hadronic matter to a quark-gluon plasma and the properties of that plasma. We have been measuring entropy densities, Debye and hadronic screening lengths, the spacial string tension and topological susceptibility in addition to the standard order parameters. The HEMCGC collaboration has simulated lattice QCD with two light staggered quarks, mq = 0.025 and mq = 0.010 on a 163 × 32 lattice. We have measured the glueball spectrum and topological susceptibilities for these runs.

We present results from simulations of lattice QCD using two flavors of dynamical Wilson fermions at a lattice coupling $\beta=5.3$ on $16^3 \times 32$ lattices at two hopping parameters, $\kappa=0.1670$ and $0.1675$, leading to $m_\pi \approx 0.44$ and $0.33$ respectively. We show spectroscopy for S-wave hadrons and compare our results to other recent simulations with dynamical Wilson fermions. (Complete postscript file can be obtained by anonymous ftp from ftp.scri.fsu.edu as file "lat92.ps" from directory "pub/heller".)

Classical methods are used to compute multi-particle production in the initial instants of a high energy heavy ion collision. Non-perturbative expressions are derived relating the distributions of produced partons to those of wee partons in the wavefunctions of the colliding nuclei. The time evolution of components of the stress-energy tensor and the impact parameter dependence of elliptic flow is studied. We discuss the space-time picture that emerges and interpret the RHIC data within this framework.

Lattice QCD with 2 light staggered quark flavours is being simulated on a $16^3\times8$ lattice to study the transition from hadronic matter to a quark gluon plasma. We have completed runs at $m_q=0.0125$ and are extending this to $m_q=0.00625$. We also examine the addition of a non-dynamical "strange" quark. Thermodynamic order parameters are being measured across the transition and further into the plasma phase, as are various screening lengths. No evidence for a first order transition is seen, and we estimate the transition temperature to be $TY_c=143(7) MeV$.

We present preliminary results from the 1991 HEMCGC simulations with staggered dynamical fermions on a $16^3 \times 32$ lattice at $\beta = 5.6$ with sea quark masses $am_q = 0.025$ and 0.01. The spectroscopy was done both for staggered valence quarks with mass equal to the sea quark masses and for Wilson valence quarks at six different values for $\kappa$, 0.1320, 0.1410, 0.1525, 0.1565, 0.1585, and 0.1600. In addition to the measurements performed in our earlier work, we also measured the $\Delta$ and other `extended' hadrons for staggered valence quarks and pseudo-scalar decay constants and vector meson matrix elements, the wave function at the origin, for Wilson valence quarks.

We show that an observable fraction of the measured elliptic flow may originate in classical gluon fields at the initial stage of a peripheral high-energy nuclear collision. This mechanism complements the contribution of late stage mechanisms, such as those described by hydrodynamics, to the observed elliptic flow.

Abstract Cancer progression involves the gradual loss of a differentiated phenotype and acquisition of progenitor and stem cell-like features. Here, we provide new stemness indices for assessing the degree of oncogenic dedifferentiation. We took advantage of an innovative one-class logistic regression machine learning algorithm (OCLR) to extract transcriptomic and epigenetic feature sets derived from non-transformed pluripotent stem cells and their differentiated progenies. Using OCLR, we were able to sort TCGA tumor samples by stemness phenotype and identify previously undiscovered biological mechanisms associated with the dedifferentiated oncogenic state. Analyses of tumor microenvironment revealed the correlation of cancer stemness with immune checkpoint expression and infiltrating immune system cells not previously anticipated. We have shown the de-differentiated oncogenic phenotype increased in the metastatic tumor that further justify their more aggressive phenotype. Application of our stemness indices reveals features of intra-tumor heterogeneity in molecular profiles obtained from the single-cell analyses. Finally, the machine learning-based indices allowed for the identification of chemical compounds and novel targets for the cancer therapies aiming at tumor differentiation. Our findings provide new prognostic signatures that enable cancer biologists and oncologists to quantify the impact of tumor stemness on outcome across cancer types and may help to pave the way for progress in treatment strategies for cancer patients. Citation Format: Tathiane M. Malta, Artem Sokolov, Andrew J. Gentles, Tomasz Burzykowski, Laila Poisson, John Weinstein, Bożena Kamińska, Joerg Huelsken, Larsson Omberg, Olivier Gevaert, Antonio Colaprico, Patrycja Czerwińska, Sylwia Mazurek, Lopa Mishra, Holger Heyn, Alex Krasnitz, Andrew K. Godwin, Alexander J. Lazar, The Cancer Genome Atlas Research Network, Joshua M. Stuart, Katherine Hoadley, Peter W. Laird, Houtan Noushmehr, Maciej Wiznerowicz. Comprehensive analysis of cancer stemness [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr LB-373.

We have studied the spectrum on lattice sizes 83, 103, 123, and 164 × 24 for 6/g2 = 5.445 and amq = 0.025. We find small finite size effects. With much smaller errors than earlier results, we find no improvement in the Edinburgh plot as the lattice spacing decreases from ≈ 0.25 fm to ≈ 0.15 fm. The improved values of the rho and nucleon masses allow a more precise determination of the temperature of chiral symmetry restoration.

We have continued our study of finite size effects in the QCD spectrum on lattices ranging in size from 83 × 24 to 163 × 24. We have increased our statistics for quark mass amq = 0.025 for the smallest lattice size. In addition, we have studied quark mass 0.0125 for lattice sizes 123 × 24 and 163 × 24. These lattice sizes correspond to a box 1.8–3.6 fm on a side when the rho mass at zero quark mass is used to set the scale. We discuss the nucleon to rho mass ratio at a smaller value of mπ/mϱ than previously studied with two dynamical flavors.

We discuss real time simulations of high energy nuclear collisions in a classical effective theory of QCD at small x. At high transverse momenta, our results match the lowest order predictions of pQCD based mini-jet calculations. We discuss novel non-perturbative behaviour of the small x modes seen at small transverse momenta.

We present results from a study of hadron thermodynamics with Wilson quarks. The crossover curve between the high and low temperature phases is determined as a function of the gauge coupling and hopping parameter on 83 × 4 lattices. Meson masses are calculated along the crossover curve, and screening lengths are determined in the vicinity of it on 83 × 16 and 82 × 16 × 4 lattices, respectively.

We present results of numerical simulations of quantum chromodynamics at finite temperature with two flavors of Kogut-Susskind quarks on the Intel iPSC/860 parallel processor. We investigate the properties of the objects whose exchange gives static screening lengths by reconstructing their correlated quark-antiquark structure.

As part of an ongoing effort to characterize the high temperature phase of QCD, we measure the quark baryon density in the vicinity of a fixed test quark and compare it with similar measurements at low temperature and at the crossover temperature. Such an observable has also been studied by the Vienna group. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at T = 0.75Tc the induced quark number shows a surprisingly large component attributable to baryonic screening. A simulation of a simple flux tube model produces results that suggest a plausible scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.

Abstract Although we have some understanding of the genetic abnormalities occurring in B-cell chronic lymphocytic leukemia (CLL) and their association with clinical outcomes, there is an incomplete comprehension of all of the mutations contributing to disease development and progression. In most abnormalities previously observed, it has been difficult to pinpoint specific candidate genes, reflecting the inadequacy of present tools for assessing chromosomal damage. We examined copy number changes in the genomes of B cells from 58 patients with CLL using a 390,000-probe microarray, enabling us to perform comparative genomic hybridization (CGH), at a resolution exceeding previously published studies. We observed at least one genomic lesion in each CLL sample and considerable variation in the number of abnormalities from case to case. Virtually all abnormalities previously reported were also observed, most of which were highly recurrent. We observed the boundaries of known events with greater clarity and identified lesions previously not described, some of which were also recurrent. A newly identified 3.6 Mb deletion at 8p21.2-p12 includes the gene TRIM 35. A second novel deletion at 2q37.1 (587kb) encompasses the gene SP100/110/140. Of the refined regions, a 249kb region at 9p21.3 spanning the CDKN2A (p16-INK4) and a 156kb region at 18q23 containing NFATC1 are particularly interesting. In the case of NFATC1, the minimal region of overlap spans that single gene. Furthermore, we tilized our arrays to examine the clonal heterogeneity of CLL within the same patient from mixed sub-populations. The presence of greater than 30% of B-cells with the CD38 cell surface marker has been associated with poor outcome in CLL. It is an open question whether this reflects genetic heterogeneity and possibly clonal evolution. To investigate this possibility, we analyzed CD38+ and CD38− fractions from individual patients and demonstrated that three out of the four patients examined had undergone clonal diversification leading to new subclones of appreciable size. Additionally, we have utilized a 2.1 million probe ultra-high density (HD2) array from NimbleGen (Madison, WI), providing us with the capability to scan the human genome for copy number changes at a resolution of a probe every 1500 bp. Utilizing the HD2 array, we are presently re-analyzing all the CLL samples in our study, and in the process are discovering many more previously unpublished lesions, several of which pinpoint single genes. We will present the results of our findings and discuss the potential applications of high resolution CGH analysis in a clinical setting.

The formulas for mean wavelengths and widths of Unresolved Transition Arrays (UTA)[1,2], have been extended to include spectator electrons and jj transitions. These were used to interpret several sorts of satellite spectra, e.g., 3d 10 nℓ q− −3d 9 4fn q transitions in atoms Tm thru W from laser produced plasmas, and 3d m 4s − 3d m−1 4p4s in Mo and Pd spectra. The Unresolved Character of the UTA will be discussed thanks to an evaluation of the number of lines in the array. This will be applied to 4d-4f transitions in Ionized Rare Earths.

Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Copy number alterations (CNAs) play an important role in molding the genomes of breast cancers and have been shown to be clinically useful for prognostic and therapeutic purposes. However, our knowledge of intra-tumoral genetic heterogeneity of this important class of somatic alterations is limited. Here, using single-cell sequencing, we comprehensively map out the facets of copy number alteration heterogeneity in a cohort of breast cancer tumors. Ou/var/www/html/elife/12-05-2020/backup/r analyses reveal: genetic heterogeneity of non-tumor cells (i.e. stroma) within the tumor mass; the extent to which copy number heterogeneity impacts breast cancer genomes and the importance of both the genomic location and dosage of sub-clonal events; the pervasive nature of genetic heterogeneity of chromosomal amplifications; and the association of copy number heterogeneity with clinical and biological parameters such as polyploidy and estrogen receptor negative status. Our data highlight the power of single-cell genomics in dissecting, in its many forms, intra-tumoral genetic heterogeneity of CNAs, the magnitude with which CNA heterogeneity affects the genomes of breast cancers, and the potential importance of CNA heterogeneity in phenomena such as therapeutic resistance and disease relapse. eLife digest Cells in the body remain healthy by tightly preventing and repairing random changes, or mutations, in their genetic material. In cancer cells, however, these mechanisms can break down. When these cells grow and multiply, they can then go on to accumulate many mutations. As a result, cancer cells in the same tumor can each contain a unique combination of genetic changes. This genetic heterogeneity has the potential to affect how cancer responds to treatment, and is increasingly becoming appreciated clinically. For example, if a drug only works against cancer cells carrying a specific mutation, any cells lacking this genetic change will keep growing and cause a relapse. However, it is still difficult to quantify and understand genetic heterogeneity in cancer. Copy number alterations (or CNAs) are a class of mutation where large and small sections of genetic material are gained or lost. This can result in cells that have an abnormal number of copies of the genes in these sections. Here, Baslan et al. set out to explore how CNAs might vary between individual cancer cells within the same tumor. To do so, thousands of individual cancer cells were isolated from human breast tumors, and a technique called single-cell genome sequencing used to screen the genetic information of each of them. These experiments confirmed that CNAs did differ – sometimes dramatically – between patients and among cells taken from the same tumor. For example, many of the cells carried extra copies of well-known cancer genes important for treatment, but the exact number of copies varied between cells. This heterogeneity existed for individual genes as well as larger stretches of DNA: this was the case, for instance, for an entire section of chromosome 8, a region often affected in breast and other tumors. The work by Baslan et al. captures the sheer extent of genetic heterogeneity in cancer and in doing so, highlights the power of single-cell genome sequencing. In the future, a finer understanding of the genetic changes present at the level of an individual cancer cell may help clinicians to manage the disease more effectively. Introduction Research into the genetics of breast tumors has yielded comprehensive portraits of the somatic alterations acquired during the evolution of breast cancer genomes. Catalogues of recurrent driver alterations have been identified using an array of technologies (Teixeira et al., 2002; Adeyinka et al., 2003; Chin et al., 2006; Sjöblom et al., 2006; Fridlyand et al., 2006; Banerji et al., 2012; Cancer Genome Atlas Network, 2012; Shah et al., 2012; Ciriello et al., 2015; Nik-Zainal et al., 2016). This information has been instrumental in furthering our understanding of the basic biology that underlies breast cancer development and has led to the development of diagnostic and prognostic tests and more importantly, the development of efficacious targeted therapies (Dawson et al., 2013). While the adoption of therapeutic strategies targeting somatic cancer alterations and the pathways they control has had a profound impact on the treatment of breast cancer (Alvarez et al., 2010), disease relapse and therapeutic resistance remain important challenges (Ma et al., 2015; Majewski et al., 2015). Recent research into these phenomena has implicated genetic heterogeneity (i.e. sub-clonal variation or intra-tumoral heterogeneity) as a common mechanism to explain recurrence and treatment failure (Toy et al., 2013; Carey et al., 2016; Miller et al., 2016). However our knowledge of intra-tumoral genetic heterogeneity is limited and thus advancing it is instrumental in combating cancer. CNAs are an important class of somatic mutations that are acquired during the evolution of breast cancer genomes (Dawson et al., 2013). Studies exploring the landscape of CNAs have considerably advanced our knowledge of breast cancer biology, with translational efforts leading to advances in the clinic. Most notably, the amplification of the ERBB2 (HER2) oncogene defines a biological subtype of breast cancers and targeting this CNA has led to the development of a multitude of efficacious therapeutic agents that have dramatically increased the survival of HER2+ patients (Arteaga and Engelman, 2014). Additionally, numerous studies have demonstrated the utility of copy number information in the prognostic stratification of breast tumors (Russnes et al., 2010; Curtis et al., 2012) and studies of the genes targeted by this class of somatic mutations have substantially advanced our understanding of breast cancer biology (Gatza et al., 2014; Cai et al., 2016). However, our knowledge of CNA intra-tumoral genetic heterogeneity is limited and given the importance of this class of somatic alterations warrants further investigation. Single-cell DNA sequencing methods have recently emerged as powerful tools for the study of intra-tumoral heterogeneity with recent applications in breast (Navin et al., 2011; Eirew et al., 2015) and other tumors (Francis et al., 2014; Bolhaqueiro et al., 2019; Bian et al., 2018) revealing novel cancer genetics and biology. Here, we present a comprehensive analysis of CNAs in breast cancer based on the sequencing of thousands of single-cell genomes across a cohort of breast tumors. Our results offer in-depth views of the magnitude of intra-tumoral CNA heterogeneity present in breast cancer genomes, reveal novel and important observations that have been missed by earlier bulk studies, highlight the unique nature of the data and its ability to retrieve novel knowledge, and provide an important foundation for the future exploration of intra-tumoral genetic heterogeneity of this important class of somatic mutations. Results Samples, annotations and sequencing Samples from sixteen patients were selected from a cohort population enrolled in two phase II open-label clinical trials conducted by the Brown University Oncology Group (BrUOG). Two pre-treatment, freshly frozen biopsies per patient were obtained. Two blood samples from normal healthy individuals were also obtained and processed (discussed below – Methods). For the tumor samples, one biopsy was subject to bulk DNA and RNA isolation for transcriptome sequencing and copy number profiling by sparse sequencing. The second biopsy was subjected to single-cell copy number analysis as described previously (Baslan et al., 2012; Baslan et al., 2015). In brief, tissue was processed to obtain a suspension of DAPI stained single-nuclei. Nuclei were subsequently flow sorted by ploidy (measured by DNA-content) for single-nucleus deposition, genome amplification and sequencing. For samples with multi-modal ploidy distributions (i.e. diploid and polyploid populations) (Figure 1—figure supplement 1A), single-nuclei were sorted and sequenced from each distribution. A mean of 116 single-nuclei per tumor sample were sequenced in multiplex fashion for a total of 2086 single-cell genomes. For each nucleus, we targeted a sequencing depth of roughly 2 million reads, sufficient to call large copy number events (>1 MB) as well as focal events such as amplifications and deletions at a resolution of roughly 300kbs . Selected patient samples were representative of various biological and clinical variables such as PAM50 subtype, ploidy, and ER/PR/HER2 status as well as other parameters such as age and tumor size (Figure 1—figure supplement 1B–D). CNAs and genetic heterogeneity of stromal, non-cancer cells Nuclei processed from the diploid (2N) distribution of sorted samples could either represent cancer cells or normal cells present in the tumor mass (i.e. normal epithelia, fibroblasts, and/or immune cells). When sequencing 2N nuclei of patient samples, we obtain copy number neutral, ‘flat’ genome profiles representative of non-cancer, stromal cells (Figure 1—figure supplement 2A). Intriguingly, we observed recurrent focal homozygous deletions on chromosomes 14 and 7, in otherwise diploid genomes (Figure 1A). Further inspection localized the deletions to T-cell receptor alpha (TCRa) and beta (TCRb) loci (Figure 1—figure supplement 2B). These deletions are the result of T-cell maturation and generated via the process of V-D-J recombination. Similarly, we observed focal homozygous deletions at the heavy and light Immunoglobulin loci (IGH and IGL) on chromosomes 14 and 22, respectively, denoting B-cells (Figure 1B). Thus, using single-nuclei copy number sequencing we can detect T- and B-cells present within the tumor mass. To gauge the sensitivity of T- and B-cell detection, we retrieved highly purified CD4+/CD8+ T-cells and CD27+/CD13+ B-cells and performed single-nuclei copy number analysis on approximately 96 nuclei for both samples with the expectation that all single-nuclei should carry their respective deletions. Deletion analysis led to a calculated detection sensitivity of ~80% and 50% for T- and B-cells, respectively (Figure 1—figure supplement 2C). This allowed the quantification of T- and B-cells in the tumor mass in our samples and led to the detection of T-cells (in varying proportions) in almost all patient samples, with B-cell infiltration limited to a subset of tumors, (Figure 1C) consistent with previous studies (Ruffell et al., 2012). Figure 1 with 3 supplements see all Download asset Open asset Genetic heterogeneity of immune cells and pseudo-diploid cells in breast cancer biopsies. (A) Genome-wide copy number view of representative single-cell T-cell genomes illustrating T-Cell Receptor alpha (TCRa) and beta (TCRb) deletions. (B) Genome-wide copy number view of representative single-cell B-cell genomes illustrating light (IGL) and heavy (IGH) immunoglobulin deletions. (C) Bar plot quantification of T-cells, B-cells, pseudo-diploid cells and other non-tumor cells identified in profiled tumor biopsies. (D) Zoomed in views of TCRa deletion breakpoints in single T-cells found in tumors biopsies (P15 and P9), blood purified CD8+/4+ T-cells, and single-leukemic cells derived from a T-cell leukemia. (E) Representative genome-wide copy number plot of a T-cell exhibiting X-chromosome loss. Insert – bar plot quantification of X-loss T-cells in ER+ and ER- tumors. Asterisk denotes statistical significance based on chi-square test (p-value=0.0047). (F) Left panel: Frequency plot of CNAs identified in a panel of 200 breast cancer genomes. Highly recurrent alterations, such as 1q gain and 16 p loss are noted. Right Panel: Representative copy number plots of pseudo-diploid single-cell genomes illustrating the occurrence of recurrent breast cancer CNAs in these cells. Figure 1—source data 1 Patient sample associated metadata. https://cdn.elifesciences.org/articles/51480/elife-51480-fig1-data1-v1.xlsx.zip Download elife-51480-fig1-data1-v1.xlsx.zip Given the importance of T-cells in emerging immunotherapies (Sharma and Allison, 2015), we performed more detailed analysis on the identified T-cells and queried whether they represent clonally expanded T-cells that have infiltrated the tumor mass, or TCRa unique, non-clonal T-cells. To gauge the specificity in detecting genetically unique T-cells using single-cell sequencing we examined the pattern of breakpoints resulting from TCRa deletions. In the purified CD4+/CD8+ T-cell nuclei (n = 95), deletion breakpoints were found distributed over 14 genomic bins and in the majority of T-cells were not shared, suggesting unique TCRa recombination events (Figure 1D and Figure 1—figure supplement 2D). Extending this breakpoint analysis to T-cells identified in patient biopsies, we found that within a given tumor none of the T-cells shared identical breakpoints, similarly suggesting that the identified T-cells were non-clonally derived and genetically distinct. This is in contrast to the breakpoints observed in nuclei derived from a T-cell leukemia which were recurrent and positionally identical across different single nuclei (Figure 1D and Figure 1—figure supplement 2E). To quantitatively corroborate these observations, we devised a breakpoint distance metric and applied it to the abovementioned T-cell groupings (Methods). Indeed, we find lower breakpoint pairwise-distance values in the single-nuclei derived from the T-cell leukemia compared to both CD8+/CD4+ T-cells and T-cells found in breast cancer biopsies (Figure 1—figure supplement 2F). All the T-cell leukemia nuclei in this analysis shared identical breakpoints, p-value<10−6, in contrast to T-cells found in tumor biopsies. In addition to the heterogeneity of the TCRa deletion breakpoints in T-cells, we observed large karyotypic abnormalities affecting some T-cell genomes (Figure 1—figure supplement 2G). These karyotypic abnormalities were represented overwhelmingly by a loss of an entire copy of the X chromosome (Figure 1E) consistent with previous karyotyping studies of proliferating lymphocytes (Nowinski et al., 1990). These X-loss T-cells, when found in the same patient sample, were genetically distinct at their respective TCRa locus as judged by the deletion breakpoints as well as the above mentioned breakpoint-distance metric (Figure 1—figure supplement 2E and F). Interestingly, T-cells displaying X-loss were found more frequently in estrogen receptor negative (ER-) compared to estrogen receptor positive (ER+) tumors (p-value=0.0047) (Figure 1E, insert). Given that BRCA1 has been shown experimentally to be associated with the process of X-inactivation (Ganesan et al., 2002) and that BRCA1-mutant tumors are mostly ER- tumors, this association is intriguing. Additionally, we and others have reported the detection of individual, aneuploid nuclei that carry non-clonal, genetically heterogeneous CNAs termed pseudo-diploids (Navin et al., 2011; Demeulemeester et al., 2016). Initially identified in two triple negative primary tumors and not their matching metastasis (Navin et al., 2011), here, we extend their observation to tumors from all four PAM50 subtypes studied (i.e. LumA, LumB, HER2+, and Basal) (Figure 1c). Interestingly, we find that some carry prototypical breast cancer CNAs such as gain of 1q and loss of 16 p (Figure 1F – right panel). The pseudo-diploids observed in our cohort however do not appear to be precursors to the clonal cancer cells constituting the tumor mass as they do not share their respective CNAs (Figure 1—figure supplement 3). We interpret the observation of these nuclei as a manifestation of the inherent genomic instability present in normal breast epithelial cells of cancer patients. Further analyses, across a larger number of single pseudo-diploid nuclei while also factoring somatic single-nucleotide variant (SNV) information, are required to definitively prove this. Thus, using single-cell sequencing we were able to detect immune cells present within the tumor mass and infer their genetic heterogeneity as well as extend the identification of pseudo-diploids to all PAM50 breast cancer subtypes and observe the occurrence of cancer associated CNAs in these cells. Genetic heterogeneity of large copy number alterations in cancer cells and the importance of dosage We then proceeded to analyze the genetic heterogeneity of large-scale CNAs present in sequenced single cancer nuclei. These events include CNAs larger than 3 MB as well as whole chromosome or arm level events. As a way of illustrating the data, we plot all single-nuclei copy number profiles from a given patient on the same graph. Doing so for tumor P5 (LumA), one can visually distinguish clonal from sub-clonal alterations by observing either one or multiple copy number states at any given genomic position, respectively (Figure 2A). For example, losses of 8 p and 18 p (recurrent CNAs in breast cancers) are found at one copy number state and are thus clonal events (Figure 2A – red arrows). Alternatively, gains at 1q and 8q (also recurrent breast cancer CNAs) as well as losses on chromosomes 13 and X are found to be sub-clonal (Figure 2A – blue arrows). For P5, computing the fraction of the genome found to be clonal/sub-clonal using a stringent threshold (minimum 10% of cells showing sub-clonality – Materials and methods), we find P5 to be sub-clonal in over half of its genome (56% sub-clonal) (Figure 2A - top bar). Extending this analysis to all tumors, we find a wide range of fractional sub-clonal values with tumors showing: (1) significant (sub-clonal at ~>40% genome – Ex: P5, P22, and P59), (2) moderate (5%–20% subclonal-- Ex: P14, P58, and P31) or (3) low levels of heterogeneity (subclonal at <5% of genome – Ex: P16, P41, P1) (Figure 2B). Representative examples of significant, moderate, and low level CNA heterogeneity samples, as illustrated for P5, are provided (Figure 2—figure supplement 1). Figure 2 with 2 supplements see all Download asset Open asset Copy number heterogeneity impacts a significant proportion of breast cancer genomes and occurs at regions in the genome that are biologically and clinically important. (A) Schematic illustration of CNA heterogeneity in tumor P5. Single-cell genomes (n = 131) are plotted on the same copy number diagram. Heterogeneous/sub-clonal regions can be identified by the presence of multiple copy number states (ex: 1q and chromosome 13). Red arrows point to representative clonal alterations. Blue arrows point to representative sub-clonal alterations. (B) Quantification of copy number heterogeneity as fraction (%) of the genome found to be sub-clonal across all sequenced biopsies. (C–H) Representative chromosome wide views of identified sub-clonal CNAs affecting: regions recurrently altered in breast cancer genomes by CNAs (C), regions containing genes of therapeutic relevance (D), regions containing genes known to be affected by somatic SNVs (E), regions with experimental evidence of involvement in breast cancer metastasis (F), regions found at three or more different copy number states (G). Gray vertical bars denote the location of genes or CNAs. (H) Distant relapse-free survival curves for cases with 1q and 8q gains that are ER+ and HER2- (n = 428). Cases are stratified based on their level of 1q or 8q gain (low vs. high). Figure 2—source data 1 Inferred integer copy number values of all single cancer nuclei sequenced for all patients. https://cdn.elifesciences.org/articles/51480/elife-51480-fig2-data1-v1.zip Download elife-51480-fig2-data1-v1.zip Importantly, regions found to be sub-clonal in tumor samples included regions: (1) known to be recurrently altered by CNAs (ex: 8 p and 13q), (2) harboring genes encoding therapeutic targets such as ESR1, CYP19A (Ellis et al., 2012), CDK6 (Turner et al., 2015), and PD-L1 (Nanda et al., 2016), (3) harboring genes known to be recurrently mutated by single nucleotide variants (SNVs) such as PIK3R1, PDGFRA, and RUNX1 (Cancer Genome Atlas Network, 2012; Nik-Zainal et al., 2016), and (4) harboring genes experimentally shown to be involved in metastasis (Valiente et al., 2014; Wagenblast et al., 2015; Ross et al., 2015; Figure 2C - F and Figure 2—figure supplement 2A). DNA-FISH was used to validate a selected subset of these alterations (Figure 2—figure supplement 2B). Importantly, for some of the alterations, we find that the sub-clonal CNAs exist at three or more distinct copy number states in different single cells, for example, 8q gains in P5 (LumA) and P22 (Basal) (Figure 2G). This may have an effect on the level of expression/dosage of genes encoded on those chromosomes and thus may affect phenotypic heterogeneity. Reasoning that the increase of dosage of genes at 8q and/or 1q might be associated with advanced disease and hence bad prognosis, we devised an analysis approach to measure the relative dosage of these events in bulk copy number datasets and test their association with patient survival in a large, carefully annotated breast cancer dataset; METABRIC (20) (Methods). Indeed, we find that 1q/8q high tumors in ER+/HER2- patients (regardless of ploidy status of the tumor genome) are associated with worst distant relapse free survival (Figure 2H and Figure 2—figure supplement 2C). Further, among the newly discovered breast cancer subgroups (IntClust, IC) groups, we find that 1q/8q high tumors are enriched in the IC9 subgroup which is associated with high-risk of late distant relapse (Rueda et al., 2019; Figure 2—figure supplement 2D). Together, these data show that heterogeneity of large copy number events can: (1) affect a large proportion of the genome in any given tumor, (2) exist at multiple levels (ex: dosage - three or more copy number states in the same tumor), and (3) that this heterogeneity can affect regions of the genome that are important for treatment or disease relapse. Multiple forms of genetic heterogeneity of focal chromosomal amplicons Focal amplifications and deletions comprise another important class of CNAs. Prototypical driver amplifications containing ERBB2, CCND1, MYC, and CCNE1, as well as less commonly identified amplifications such as PPM1D and MDM2, were identified in our patient cohort and in some cases were clonal (i.e. identified in all single-nuclei sequenced) (Figure 3A and Figure 3—figure supplement 1A). However, as seen with larger CNAs, many tumors displayed chromosome amplifications genetic heterogeneity. For example in tumor P22 (basal), three focal amplicons encompassing the VEGFA, MYC and CCNE1 loci were found in varying proportions and in certain instances (VEGFA and CCNE1) in a mutually exclusive manner in sequenced single-nuclei (p-value=0.003 – Fisher’s Exact Test). A sub-population lacking any of the amplicons, but having lost an additional copy of the RB1 gene via a focal deletion was also identified (Figure 3B and C and Figure 3 – figure supplement B-D). Interestingly, the amplifications segregate with genetically distinct, geographically resolved tumor sub-populations (Figure 3—figure supplement 1D and E). Thus, P22 amplifications are somatically mosaic. Other examples of amplicon mosaicism include P5 (LumA) where an amplification targeting GATA6 was found only in a sub-population of cancer cells and P59 (Basal), where amplifications on multiple chromosomes (chromosomes 3, 5, 6 and 18) targeting important genes such as LOX (Cox et al., 2015) and PRDM1 (Nik-Zainal et al., 2016) where found in the majority of cells but absent in others (Figure 3—figure supplement 2A). In total, 6 out of the 16 (37%) tumors analyzed displayed amplicon mosaicism in the form of presence/absence of one or more amplicons in different subpopulations of cancer cells. Figure 3 with 2 supplements see all Download asset Open asset Different forms of genetic heterogeneity in chromosomal amplifications. (A) Representative zoom-in chromosome views of clonal prototypical breast cancer amplicons such as ERBB2 and CCND1 identified in patient samples. (B) Genome-wide copy number profiles of representative (n = 4) single-cell genomes illustrating heterogeneous amplifications in tumor P22. Profiles are annotated with distinguishing amplicons. A representative profile of a single nucleus with no amplifications, but deleted for the RB1 gene, is also noted. (C) Heatmap illustration of P22 amplicon copy number heterogeneity and the mutually exclusive nature of the CCNE1 and VEGFA amplicons - statistical significance based on Fisher’s Exact Test (p-value=0.0032, Odds ratio = 0, 95% confidence interval 0–0.44). Single-nuclei are ordered according to hierarchal clustering as illustrated in Figure 3—figure supplement 1D. Color key is according to increasing copy number states. (D) Genome-wide copy number profiles of representative single-cell genomes illustrating heterogeneous amplifications in tumor P6. Profiles with distinguishing amplifications are annotated on the figure. (E) DNA-FISH validation of somatic mosaicism of the SKIL and MYC amplicons in tumor P6. DNA-FISH data also illustrate the geographic demarcation of the amplification in the field of view. (F) Zoom-in-views of the SKIL and MYC amplicons in representative single-cells illustrating the heterogeneity in the level of chromosomal amplification in tumor P6. (G) DNA-FISH validation of low level/high-level amplification of SKIL and MYC loci inferred based on fluorescence signal intensity. Presence or absence of an amplicon in single cells was not the only form of variation we observed in chromosomal amplifications. Another form of variation observed came in the form of the level (or dosage) of amplification. An example is P6 (HER2+) where different spatially resolved sub-populations were identified carrying either: (1) only ERBB2 amplification, (2) ERBB2 and SKIL amplifications, or (3) ERBB2, SKIL, and MYC amplifications (Figure 3D and E). Importantly, for the SKIL and MYC amplicons, different single-nuclei were found to have varying levels/dosage of amplification. Where in some single-nuclei, SKIL and MYC levels reached over 60 copies, in others the level of amplification was less pronounced. For the MYC locus for example certain subpopulations contained MYC amplifications at less than 30 copies (Figure 3F). This was confirmed using DNA-FISH analysis based on fluorescence signal intensity (Figure 3G). This heterogeneity in amplicon level/dosage was also observed for the ERBB2 locus in another one of the six HER2 amplified tumors we analyzed (Figure 3—figure supplement 2B and C). Thus, chromosomal amplicons can exist at different levels within different single cells in a tumor mass. We also observed homozygous deletions affecting known breast cancer genes such as MLLT4, MAP2K2, and NCoR1, among others (Cancer Genome Atlas Network, 2012; Nik-Zainal et al., 2016; Figure 3—figure supplement 2D). However, we did not observe heterogeneity in this class of CNAs. We cannot rule out genetic heterogeneity of this form of variation since homozygous deletions are generally smaller in size than chromosomal amplifications and at the resolution of our analysis may have gone undetected. Nonetheless, our results illustrate varied forms of genetic heterogeneity in chromosomal amplicons affecting important breast cancer genes in a significant proportion of breast tumors. These observations are particularly important given that driver cancer genes commonly found in amplicons are generally perceived to be good targets for drug development (Cancer Genome Atlas Network, 2012), have been found to be associated with metastatic breast cancer (Bertucci et al., 2019), and because sub-clonality of amplifications is difficult to infer from bulk sequence data (especially targeted sequencing) given its quantitative nature, as opposed to qualitative nature of SNVs. Single-cell genome sequencing and multi-region sampling yield complementary information Previous studies utilizing multi-region sequencing to investigate somatic SNVs in breast and lung cancer have shown that a significant proportion of the variation that is found between different spatially resolved biopsies can be detected at the sub-clonal level in one of the biopsies with deeper sequencing (de Bruin et al., 2014; Zhang et al., 2014; Yates et al., 2015). This has not been investigated in a genome-wide, unbiased manner for CNAs. For 9 of the 16 tumors analyzed, we were able to sequence and compare bulk DNA from two spatially resolved biopsies for CNAs. In concordance with previous studies, we find substantial differences in CNAs between biopsies (Yates et al., 2015). Interestingly however, we find that much of the variation observed between the two biopsies can also be observed as sub-clonal variation in the single-cell data (Figure 4A and Figure 4—figure supplement 1). For example, in tumor P22 (Basal), differences on chromosomes 8, 12, 15 and X were observed between the two bulk profiles but were also observed sub-clonally at the single-cell level (Figure 4A and Figure 4—figure supplement 1A and B). Of 54 alterations differentially found in the two analyzed biopsies from the nine patients, 35 (65%) were identified in the data from single nuclei. This was observed for broad copy number events as well as focal amplifications, for example CCNE1 and GATA3 (Figure 4B). Importantly, additional heterogeneous CNAs were detected only in the single-cell data and not in the bulk comparisons, for example variation on chromosome 1q and 1 p in P22 as well as alterations on 1q and chromosome four in P5, with the con

The dynamics of low-x partons in the transverse plane of a high-energy nuclear collision is classical, and therefore admits a fully non-perturbative numerical treatment. The authors report results of a recent study estimating the initial energy density in the central region of a collision. Preliminary estimates of the number of gluons per unit rapidity, and the initial transverse momentum distribution of gluons, are also provided.

We report results of our ongoing nonperturbative numerical study of a classical effective theory describing low-x partons in the central region of a heavy-ion collision. In particular, we give estimates of the initial transverse energies and multiplicities for a wide range of collision regimes, including those at RHIC and at LHC.

The dynamics of low-x partons in the transverse plane of a high-energy nuclear collision is classical, and therefore admits a fully non--perturbative numerical treatment. We report results of a recent study estimating the initial energy density in the central region of a collision. Preliminary estimates of the number of gluons per unit rapidity, and the initial transverse momentum distribution of gluons, are also provided.

We report results of our ongoing nonperturbative numerical study of a classical effective theory describing low-x partons in the central region of a heavy-ion collision. In particular, we give estimates of the initial transverse energies and multiplicities for a wide range of collision regimes, including those at RHIC and at LHC.

At very high energies, the high parton densities (characterized by a semi-hard saturation scale \Lambda_s) ensure that parton distributions can be described by a classical effective field theory with remarkable properties analogous to those of spin glass systems. This color glass condensate (CGC) of gluons also provides the initial conditions for multi-particle production in high energy nuclear collisions. In this talk, we briefly summarize recent theoretical and phenomenological progress in the CGC approach to small x physics. In particular, we discuss recent numerical work on the real time gluodynamics of partons after a nuclear collision. The implications of this work for the theoretical study of thermalization in nuclear collisions and on the phenomenological interpretation of results of the recent RHIC experiments are also discussed.

We discuss real time simulations of high energy nuclear collisions in a classical effective theory of QCD at small x. At high transverse momenta, our results match the lowest order predictions of pQCD based mini-jet calculations. We discuss novel non-perturbative behaviour of the small x modes seen at small transverse momenta.

We argue that the classical evolution of small x modes in the collision of two ultrarelativistic nuclei is described on a transverse lattice by the Kogut--Susskind Hamiltonian in 2+1-dimensions coupled to an adjoint scalar field. The initial conditions for the evolution are provided by the non--Abelian Weizsäcker--Williams fields which constitute the classical parton distributions in each of the nuclei. We outline how lattice techniques developed for real time simulations of field theories in thermal equilibrium can be used to study non--perturbatively, thermalization and classical gluon radiation in ultrarelativistic nuclear collisions.

The authors discuss a real time, non-perturbative computation of the transverse dynamics of gluon fields at central rapidities in very high energy nuclear collisions.

At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial ``formation'' time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.

We discuss a real time, non-perturbative computation of the transverse dynamics of gluon fields at central rapidities in very high energy nuclear collisions.

At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial formation time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.

Quantum chromodynamics, the theory of the interaction of quarks and gluons, can be simulated on modern su percomputers. Using the Hybrid algorithm on a 12 4 spacetime lattice, the High Energy Monte Carlo Grand Challenge (HEMCGC) group has recently performed the most realistic calculation of the hadronic spectrum to date. The inclusion of the effects of light virtual quark antiquark pairs leads to a significant improvement over previous work. Achievement of these results required innovative work in basic theoretical physics, algorithm design, and software development. The next decade of progress in this challenging field will require machines several orders of magnitude more capable than today's supercomputers.

X-ray spectra of highly ionized atoms (Tm to Pt) emitted from Laser produced plasma are characterized by the simple structure given by resonant transitions of the Nil-like ions, accompanied by the more complex pattern of satellite transitions emitted by ions in the neighbouring states of ionization. An analysis of these structures has been given recently for the satellites of the 3d 10 − 3d 9 4p[l] and of the 3p 6 3d l0 − 3p 5 3d 10 4s, 4d[2] transitions of the Nil-like inns. However, most of the radiation emitted in this spectral range [4–10Å] concentrate in a wide, rather structureless satellite feature in the long wavelength side of the 3d 10 −3d 9 4f Ni-I like transition, on which some lines are superimposed. Line identification has been achieved successfully with the methods of [1], [2] and will be published separately. In this communication, we deal only with the pseudocontinuum.

The effect of field configuration copying on both a fermion and a fermion-antiferium pair correlation functions is studied in a simple quantum-mechanical model. It is found that the copying procedure generally results in a large correction to the corresponding effective masses. In particular, this correction leads to an oscillatory behavior of the effective masses, similar to that observed for mesons in recent lattice QCD calculations. It is argued that the copying technique is unlikely to be useful as a spectroscopic tool.

Quantum chromodynamics (QCD) predicts that at very high temperature there is a phase transition or cross over from the low-temperature state of ordinary matter to a high-temperature state consisting of a plasma of quarks and gluons. The nature of this transition and the properties of the high-temperature phase are im portant for an understanding of cosmology, heavy ion collisions, and the structure of QCD itself. The study of high-temperature QCD is one of the major goals of lattice gauge theory. Such studies involve large-scale computer simulations. We briefly review the status of this subject and present preliminary results from a large-scale study in progress on the Pittsburgh Super computer Center's Connection Machine (CM-2).

Performance of the Intel iPSC/860 parallel processor for Quantum Chromodynamics codes with dynamical fermions is described. After reviewing the hardware and software environments provided by the manufacturer, the data structures appropriate for the QCD code are described. Techniques for maximum performance are briefly discussed. We achieve a speed of 10–15 Mŕlops per node depending upon how many lattice sites are located on each node.

The effect of field configuration copying on both fermion and fermion-antifermion pair correlation functions is studied in detail in a simple quantum-mechanical model. It is found that, with very few exceptions, the copying procedure results in a large correction to the corresponding effective masses. In particular, this correction leads to an oscillatory behavior of the effective masses, similar to that observed for mesons in recent lattice QCD calculations. It is argued that the copying technique is unlikely to be useful as a spectroscopic tool.

We report on studies of simple matrix elements from simulations with two flavors of sea quarks, both staggered and Wilson. We show the decay constants of vector and pseudoscalar mesons. The effects of sea quarks are small. These simulations are done at relatively large lattice spacing compared to most quenched studies.

Under the DOE Grand Challenge program, we have calculated the hadron spectrum of QCD with two flavors of dynamical quarks. We set 6g2 = 5.6 and use bare quark masses amq = 0.025 and 0.01 to generate gauge configurations. The spectrum is calculated using both staggered and Wilson valence quarks. There are several positive features when these results are compared to those with larger lattice spacing; however, the nucleon to rho mass ratio is still too large.

As part of an ongoing effort to characterize the high temperature phase of QCD, we measure the quark baryon density in the vicinity of a fixed test quark and compare it with similar measurements at low temperature and at the crossover temperature. Such an observable has also been studied by the Vienna group. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at T = 0.75 T_c the induced quark number shows a surprisingly large component attributable to baryonic screening. A simulation of a simple flux tube model produces results that suggest a plausible scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.