Detection of minimal residual disease (MRD) in cancer patients after surgery can provide an early marker for disease recurrence and guide subsequent treatment decisions. Accurate and sensitive estimation of tumour burden after cancer surgery may be obtained through liq- uid biopsies, measuring circulating tumour DNA (ctDNA) using, for example, mutation-based Variant Allele Frequency (VAF) values. However, to be applicable to all patients this ei- ther requires tumour-informed, patient-specific mutation panels or sensitive, tumour-agnostic genome-wide measurements. We propose a solution that accounts for patient-specific charac- teristics in genome-wide screens. For that, we introduce a bivariate deconvolution model to estimate tumour proportion from circulating cell-free DNA (cfDNA) methylation profiles of patients before and after surgery. The observations are modelled as a convolution of two bivariate latent variables, corresponding to tumour and background signals, mixed by the tumour proportion at each measurement. This bivariate approach links pre- and post-surgery measurements improving estimation of the tumour proportion after surgery, when the tumour signal is potentially v
The re-solidification of amorphous solids after mechanically driven yielding from a nonequilibrium state is a fundamental soft matter science problem of broad relevance in materials science, with implications for material strength, processing, and printing-based additive manufacturing. We present a microscopic statistical mechanical theory that predicts in a unified manner the coupled time evolutions of structural and stress recovery following shear cessation from a mechanically prepared nonequilibrium state. The approach is built on recent advances in understanding activated dynamics in Brownian systems under both quiescent and startup continuous shear conditions. A particle-level microrheological model framework self-consistently incorporates stress generation, constraint softening due to external mechanical forces and structural deformation. After flow cessation, the theory captures the re-building of kinetic constraints and activation barriers over time that underlie structural recovery, stress relaxation, and re-solidification through dynamic relaxation and an elementary form of convective elastic backflow. The ideas are general for particle-based materials, and quantitatively
The paper shows how to determine the loss on an LGD borrower's loan after default, with or without preparation of a separate model. LGD after default is estimated taking into account the average repayment period of the defaulted loan, knowledge of volumes, moments of default and repayments, the rate or other parameters in the vector of determinants. The calculation of the average repayment period for overdue loans is given in the article. A Bayesian scheme is used to estimate repayable debts, considering the percentage of repayment. A general recovery model was used for the LGD segment recovery process. Only this type of model allows you to set LGD less than or equal to 1, which is required for further estimates.
In recent years the coincidence of the operator relations equivalence after extension and Schur coupling was settled for the Hilbert space case, by showing that equivalence after extension implies equivalence after one-sided extension. In this paper we investigate consequences of equivalence after extension for compact Banach space operators. We show that generating the same operator ideal is necessary but not sufficient for two compact operators to be equivalent after extension. In analogy with the necessary and sufficient conditions on the singular values for compact Hilbert space operators that are equivalent after extension, we prove the necessity of similar relationships between the $s$-numbers of two compact Banach space operators that are equivalent after extension, for arbitrary $s$-functions. We investigate equivalence after extension for operators on $\ell^{p}$-spaces. We show that two operators that act on different $\ell^{p}$-spaces cannot be equivalent after one-sided extension. Such operators can still be equivalent after extension, for instance all invertible operators are equivalent after extension, however, if one of the two operators is compact, then they cannot b
We develop a theoretical formalism for time-dependent radiative heat flux from one object to another in the case where the former starts radiating at a certain time. The time dependence is demonstrated for the heat flux between two isolated nanoparticles. After one particle starts radiating, the emitted energy first reaches the other one with a delay according to electromagnetic retardation, and afterwards the flux exhibits oscillatory exponential relaxation to its stationary value. For the room- or higher-temperature radiation, the oscillation period and relaxation time are determined by the resonance frequency and damping rate of the particle polarizability, respectively, being equal to dozens of femtoseconds and one picosecond for silicon carbide particles. At cryogenic temperatures, the relaxation time depends on the thermal wavelength.
The Neural Tangent Kernel (NTK) is the wide-network limit of a kernel defined using neural networks at initialization, whose embedding is the gradient of the output of the network with respect to its parameters. We study the "after kernel", which is defined using the same embedding, except after training, for neural networks with standard architectures, on binary classification problems extracted from MNIST and CIFAR-10, trained using SGD in a standard way. For some dataset-architecture pairs, after a few epochs of neural network training, a hard-margin SVM using the network's after kernel is much more accurate than when the network's initial kernel is used. For networks with an architecture similar to VGG, the after kernel is more "global", in the sense that it is less invariant to transformations of input images that disrupt the global structure of the image while leaving the local statistics largely intact. For fully connected networks, the after kernel is less global in this sense. The after kernel tends to be more invariant to small shifts, rotations and zooms; data augmentation does not improve these invariances. The (finite approximation to the) conjugate kernel, obtained us
Cells of human buccal epithelium of 6 male donors were exposed to microwave radiation (frequency f=36,64 GHz, power density E = 10, 100, and 400 mcW/cm^2). Exposure time in all experiments was 10 seconds. Heterochromatin was stained by 2% orcein in 45 % acetic acid. The stainability of cells with trypan blue (0,5 %) and indigocarmine (5 mM) after 5 min of staining was investigated. Irradiation induced chromatin condensation (increase of number of heterochromatin granules) and increase of membrane permeability to vital dyes trypan blue and indigocarmine. Isolated human buccal cells had shown the ability to recover these changes. Number of heterochromatin granules lowered to initial level after 0,5 hour (E = 10 mcW/cm^2) and 2 hours (E = 100, and 400 mcW/cm^2) after irradiation. Cell plasma membrane permeability recovered a bit later, in correspondence, after 1 hour and 3 hours after irradiation.
JWST observations confirm the existence of galaxies as early as 300Myr and at a higher number density than expected based on galaxy formation models and HST observations. Yet, sources confirmed spectroscopically in the first 500Myr have estimated stellar masses $<5\times10^8M_\odot$, limiting the signal to noise ratio (SNR) for investigating substructure. We present a high-resolution spectroscopic and spatially resolved study of a rare bright galaxy at $z=9.3127\pm0.0002$ with a stellar mass of $(2.5^{+0.7}_{-0.5})\times10^9M_\odot$, forming $25^{+3}_{-4}M_\odot/yr$ and with a metallicity of $\sim0.1Z_\odot$- lower than in the local universe for the stellar mass but in line with expectations of chemical enrichment in galaxies 1-2Gyr after the Big Bang. The system has a morphology typically associated to two interacting galaxies, with a two-component main clump of very young stars (age$<10$Myr) surrounded by an extended stellar population ($130\pm20$Myr old, identified by modeling the NIRSpec spectrum) and an elongated clumpy tidal tail. The spectroscopic observations identify O, Ne and H emission lines, and the Lyman break, where there is evidence of substantial Ly$α$ absorpt
The detection of delayed emission at X-ray optical and radio wavelengths, ``after-glow'', suggests that the relativistic shell which emitted the initial GRB due to internal shocks decelerates on encountering an external medium, giving rise to the after-glow. At a very early stage (few seconds), the observed bolometric luminosity increases as t^2. On longer time scales (more than about 10s), the luminosity drops as t^{-1}. If the main burst is long enough, an intermediate stage of constant luminosity will form. In this case, the after-glow overlaps the main burst, otherwise there is a time separation between the two. On the long time scale, the flow decelerate in a self similar way, reaching non relativistic velocities after about 30days. Due to the deceleration and the accumulation of ISM material, the relation between the observed time, the shock radius, and its Lorentz factor, is given by t=R/16γ^2c which is a factor of 8 different from the usual expression. The majority of particles are those of the original ejecta (and not the ISM) up to about 900s. These particles reach sub-relativistic velocities on a time scale of about 2hours, well before the flow becomes sub-relativistic.
This paper presents a comprehensive study of post-mortem human iris recognition carried out for 1,200 near-infrared and 1,787 visible-light samples collected from 37 deceased individuals kept in the mortuary conditions. We used four independent iris recognition methods (three commercial and one academic) to analyze genuine and impostor comparison scores and check the dynamics of iris quality decay over a period of up to 814 hours after death. This study shows that post-mortem iris recognition may be close-to-perfect approximately 5 to 7 hours after death and occasionally is still viable even 21 days after death. These conclusions contradict the statements present in past literature that the iris is unusable as a biometrics shortly after death, and show that the dynamics of post-mortem changes to the iris that are important for biometric identification are more moderate than previously hypothesized. The paper contains a thorough medical commentary that helps to understand which post-mortem metamorphoses of the eye may impact the performance of automatic iris recognition. We also show that post-mortem iris recognition works equally well for images taken in near-infrared and when the
Until recently the positions of gamma ray bursts were not sufficiently well known within a short timescale to localize and identify them with known celestial sources. Following the historical detection of the X-ray afterglow of the burst GRB970228, extending from 30 s to 3 days after the main peak, by the Beppo-SAX satellite and that of an optical transient 21 hr after the burst, we report here the detection of the same optical transient, in images obtained only 16 hours after the burst.
There is increasing evidence that causality provides useful bounds in determining the domain structure after a continuous transition. In devising their scaling laws for domain size after such a transition, Zurek and Kibble presented arguments in which causality is important both before and after the time at which the transition begins to be implemented. Using numerical simulations of kinks in 1+1 dimensions, we explain how the domain structure is determined exclusively by what happens after the transition, even though the correlation length freezes in before the transition.
We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.
Consider a finite undirected unweighted graph G and add a new node to it arbitrarily connecting it to pre-existing nodes. We study the behavior of the Perron eigenvalue of the non-backtracking matrix of G before and after such a node addition. We prove an interlacing-type result for said eigenvalue, namely, the Perron eigenvalue never decreases after node addition. Furthermore, our methods lead to bounds for the difference between the eigenvalue before and after node addition. These are the first known bounds that have been established in full rigor. Our results depend on the assumption of diagonalizability of the non-backtracking matrix. Practical experience says that this assumption is fairly mild in many families of graphs, though necessary and sufficient conditions for it remain an open question.
To perform inference after model selection, we propose controlling the selective type I error; i.e., the error rate of a test given that it was performed. By doing so, we recover long-run frequency properties among selected hypotheses analogous to those that apply in the classical (non-adaptive) context. Our proposal is closely related to data splitting and has a similar intuitive justification, but is more powerful. Exploiting the classical theory of Lehmann and Scheffé (1955), we derive most powerful unbiased selective tests and confidence intervals for inference in exponential family models after arbitrary selection procedures. For linear regression, we derive new selective z-tests that generalize recent proposals for inference after model selection and improve on their power, and new selective t-tests that do not require knowledge of the error variance.
We use lattice simulations to examine the detailed dynamics of inflaton fragmentation during and after preheating in $λφ^4$ chaotic inflation. The dynamics are qualitatively similar to preheating after $m^2 φ^2$ inflation, involving the exponential growth and subsequent expansion and collision of bubble-like inhomogeneities of the inflaton and other scalar fields. During this stage fluctuations of the fields become strongly non-Gaussian. In the quartic theory, the conformal nature of the theory allows us to extend our simulations to much greater times than is possible for the quadratic model. With these longer simulations we have been able to determine the time scale on which Gaussianity is restored, which occurs after a time on the order of a thousand inflaton oscillations.
After recalling some puzzles in cosmology and briefly reviewing the Friedmann-Lemaître cosmos a simple unified model of the ``Dark Sector'' is described. This model involves a scalar field and a pseudo-scalar axion field that give rise to Dark Energy in the form of ``quintessence'' and to ``fuzzy'' Dark Matter, respectively. Predictions of the model concerning the late-time evolution of the Universe and possible implications for the problem of the observed Matter-Antimatter Asymmetry in the Universe are sketched.
We investigate the dynamics of the XXZ spin chain after a geometric quench, which is realized by connecting two half-chains prepared in their ground states with zero and maximum magnetizations, respectively. The profiles of magnetization after the subsequent time evolution are studied numerically by density-matrix renormalization group methods, and a comparison to the predictions of generalized hydrodynamics yields a very good agreement. We also calculate the profiles of entanglement entropy and propose an ansatz for the noninteracting XX case, based on arguments from conformal field theory. In the general interacting case, the propagation of the entropy front is studied numerically both before and after the reflection from the chain boundaries. Finally, our results for the magnetization fluctuations indicate a leading order proportionality relation to the entanglement entropy.
We study Waelbroeck's category of Banach quotients after Wegner, focusing on its basic homological and functional analytic properties.
We investigate the dynamics of the Standard Model higgs with a minimal coupling to gravity during and after inflation. In the regime where the Standard Model vacuum is stable, we find that the higgs becomes a light spectator field after about 30 efolds of inflation, irrespectively of its initial value. Once the higgs has become light, its root-mean-square value h_* relaxes to equilibrium in about 85 efolds for the inflationary scale of H_*=10^4 GeV and in 20 efolds for H_*=10^10 GeV. The equilibrium value is given by h_*~0.36 lambda^{-1/4}H_*, where lambda=0.09 ... 0.0005 is the higgs self coupling at the scales H_*=10^4 ... 10^10 GeV. We show that the main decay channel of the higgs condensate after inflation is the resonant production of Standard Model gauge bosons. For a set of parameters we find that a significant part of the condensate has decayed in between 340 and 630 Hubble times after the onset of higgs oscillations, depending on H_* in a non-trivial way. The higgs perturbations correspond to isocurvature modes during inflation but they could generate significant adiabatic perturbations at a later stage for example through a modulation of the reheating stage. However, this