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Metastatic prostate cancer (mPC) comprises a spectrum of diverse phenotypes. However, the extent of inter- and intra-tumor heterogeneity is not established. Here we use digital spatial profiling (DSP) technology to quantitate transcript and protein abundance in spatially-distinct regions of mPCs. By assessing multiple discrete areas across multiple metastases, we find a high level of intra-patient homogeneity with respect to tumor phenotype. However, there are notable exceptions including tumors comprised of regions with high and low androgen receptor (AR) and neuroendocrine activity. While the vast majority of metastases examined are devoid of significant inflammatory infiltrates and lack PD1, PD-L1 and CTLA4, the B7-H3/CD276 immune checkpoint protein is highly expressed, particularly in mPCs with high AR activity. Our results demonstrate the utility of DSP for accurately classifying tumor phenotype, assessing tumor heterogeneity, and identifying aspects of tumor biology involving the immunological composition of metastases. The inter- and intra-tumor heterogeneity of metastatic prostate cancer (mPC) is underexplored. Here the authors use Digital Spatial Profiling to study gene and protein expression heterogeneity in 27 mPC patients, finding variation in associated pathways and potential immunotherapy targets.

Digital Spatial Profiling (DSP) is a method for highly multiplex spatial profiling of proteins or RNAs suitable for use on formalin-fixed, paraffin-embedded (FFPE) samples. The approach relies on (1) multiplexed readout of proteins or RNAs using oligonucleotide tags; (2) oligonucleotide tags attached to affinity reagents (antibodies or RNA probes) through a photocleavable (PC) linker; and (3) photocleaving light projected onto the tissue sample to release PC oligonucleotides in any spatial pattern across a region of interest (ROI) covering 1 to ~5,000 cells. DSP is capable of single-cell sensitivity within an ROI using the antibody readout, with RNA detection feasible down to ~600 individual mRNA transcripts. We show spatial profiling of up to 44 proteins and 96 genes (928 RNA probes) in lymphoid, colorectal tumor and autoimmune tissues by using the nCounter system and 1,412 genes (4,998 RNA probes) by using next-generation sequencing (NGS). DSP may be used to profile not only proteins and RNAs in biobanked samples but also immune markers in patient samples, with potential prognostic and predictive potential for clinical decision-making. A turnkey system allows for spatial profiling of proteins and RNA in fixed tissues, providing a window on cellular heterogeneity.

In compressed sensing, one takes [Formula] samples of an N -dimensional vector [Formula] using an [Formula] matrix A , obtaining undersampled measurements [Formula]. For random matrices with independent standard Gaussian entries, it is known that, when [Formula] is k -sparse, there is a precisely determined phase transition: for a certain region in the ([Formula],[Formula])-phase diagram, convex optimization [Formula] typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k -sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to [Formula] for four different sets [Formula], and the results establish our finding for each of the four associated phase transitions.

The addition of HER2-targeted agents to neoadjuvant chemotherapy has dramatically improved pathological complete response (pCR) rates in early-stage, HER2-positive breast cancer. Nonetheless, up to 50% of patients have residual disease after treatment, while others are likely overtreated. Here, we performed multiplex spatial proteomic characterization of 122 samples from 57 HER2-positive breast tumors from the neoadjuvant TRIO-US B07 clinical trial sampled pre-treatment, after 14-21 d of HER2-targeted therapy and at surgery. We demonstrated that proteomic changes after a single cycle of HER2-targeted therapy aids the identification of tumors that ultimately undergo pCR, outperforming pre-treatment measures or transcriptomic changes. We further developed and validated a classifier that robustly predicted pCR using a single marker, CD45, measured on treatment, and showed that CD45-positive cell counts measured via conventional immunohistochemistry perform comparably. These results demonstrate robust biomarkers that can be used to enable the stratification of sensitive tumors early during neoadjuvant HER2-targeted therapy, with implications for tailoring subsequent therapy.

Asynchronous digital circuits are circuits that don't have clocks. They sometimes have advantages including speed, lower power consumption, and relative insensitivity to environmental conditions such as temperature. Transient faults, which are changes in the circuit that do not permanently damage the circuit, are a growing problem in digital circuits. Transient faults are mainly due to radiation effects such as Single Event Upsets (SEUs). These faults occur on the ground and are exacerbated in space.In this work, I present an overview of asynchronous circuits, in particular speed-independent control circuits, and our model for transient faults. I then present a fault-tolerant transformation of the circuit based on duplication. I discuss how to define fault tolerance formally. Then I show using logic and formal methods why the transformed circuit is fault-tolerant to single transient faults.

We survey classical localization problems arising from quantum network models in symmetry class C and their mappings to history-dependent random walks on directed lattices. We describe how localization versus delocalization of trajectories can be analysed using percolation methods and combinatorial enumeration of path intersection patterns. In particular, we review results establishing almost sure finiteness of trajectories for parameters near criticality and polynomial bounds on the confinement length in cylindrical geometries.

Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite the elementary update rules, LLGs exhibit rich dynamical regimes: typically, trajectories close quickly and the distribution of loop lengths has exponential tails, but at special concentrations of scatterers one observes critical behavior with scale-free statistics and fractal geometry. This survey focuses on the critical behavior of closed trajectories in two-dimensional LLGs, starting from the numerical study of Cao and Cohen, and its relation to percolation-hull scaling and kinetic hull-generating walks. We highlight the scaling hypothesis for loop-length distributions, the emergence of critical exponents \\(\\tau=15/7\\), \\(d_f=7/4\\), and \\(\\sigma=3/7\\) in several universality classes, and the appearance of alternative exponents in partially occupied models.

Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies principal transport regimes through quantitative observables (velocity, diffusivity, mean-square displacement, first-passage, large deviations, aging), and reviews core methods in one dimension (potential/valley mechanisms) and in higher dimensions (environment-seen-from-the-particle, correctors/homogenization, regeneration and ballisticity criteria).

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and nonequilibrium phase transitions, transport and hydrodynamic limits, kinetic roughening, self-organized criticality, and complex spatiotemporal correlations. This survey focuses on three tightly connected themes. \\emph{(i)} We present a structural view of CA as shift-commuting maps on configuration spaces, emphasizing rule complexity, reversibility, and conservation laws (including discrete continuity equations). \\emph{(ii)} We organize transport in CA into ballistic, diffusive, and anomalous regimes, and connect microscopic currents to macroscopic laws through Green--Kubo formulas, scaling theory, and universality classes. \\emph{(iii)} We develop correlation-based methods -- from structure factors and response formulas to computational mechanics and data-driven inference -- that diagnose regimes and enable coarse-graining.

We have developed Digital Spatial Profiling (DSP), a non-destructive method for high-plex spatial profiling of proteins and RNA, using oligonucleotide detection technologies with unlimited multiplexing capability. The key breakthroughs underlying DSP are threefold: (1) multiplexed readout of proteins/RNA using oligo-tags; (2) oligo-tags attached to affinity reagents (antibodies/RNA probes) through a photocleavable (PC) linker; (3) photocleaving light projected onto the tissue sample to release PC-oligos in any spatial pattern. Here we show precise analyte reproducibility, validation, and cellular resolution using DSP. We also demonstrate biological proof-of-concept using lymphoid, colorectal tumor, and autoimmune tissue as models to profile immune cell populations, stroma, and cancer cells to identify factors specific for the diseased microenvironment. DSP utilizes the unlimited multiplexing capability of modern genomic approaches, while simultaneously providing spatial context of protein and RNA to examine biological questions based on analyte location and distribution.