State transitions during outbursts of black hole X-ray binaries exhibit complex, rapidly evolving disk-corona coupling. Understanding this dynamic phase is essential for deciphering accretion physics and the mechanisms that drive outbursts, yet it remains poorly understood due to the scarcity of high-quality/-cadence observations. Here, we present an analysis of observations by the Hard X-ray Modulation Telescope (HXMT) during the 2023 outburst of the newly discovered low-mass black hole X-ray binary Swift J1727.8-1613. Follow-up, high-cadence monitoring reveals pronounced variability in disk emission, attributable to fluctuations in the accretion rate. These disk fluctuations exhibit damped amplitudes and shortened flare periods. This evolving disk emission modulates the supply of soft seed photons to the corona, leading to a dynamically changing positive correlation between the photon index $Γ$ and the Comptonization luminosity $L_{\rm Comp}$. As the transition proceeds, the correlation shifts toward higher $Γ$ and a narrower range of $L_{\rm Comp}$. We further suggest that the damped disk variability arises from fluctuations generated at large disk radii and propagating inward, possibly linked to the thermal-viscous disk instability.

The Abels-Margulis-Soifer lemma states that if a semigroup $Γ$ acts strongly irreducibly by linear transformations on a finite-dimensional real vector space, then any element of $Γ$ can be multiplied by an element of some fixed finite subset of $Γ$ so that it becomes proximal (i.e. it acts on the corresponding projective space with an attracting fixed point and a repelling projective hyperplane) and even uniformly proximal (i.e. the distance between the attracting fixed point and the repelling projective hyperplane is uniformly bounded from below and the contraction towards the attracting fixed point is uniformly strong). We prove a version of this lemma simultaneously for linear representations of a semigroup $Γ$, acting on the corresponding projective spaces, and for representations of $Γ$ to isometry groups of (not necessarily proper) Gromov hyperbolic metric spaces, acting on the corresponding Gromov boundaries.

Extreme mass-ratio inspirals (EMRIs) are binary systems where a compact object slowly inspirals into its much larger compact partner. Since we anticipate such systems to exist within and be dynamically influenced by the galactic center environment, we expect them to be instrumental in studying these environments and testing our theories of gravity in the strong field regime. The gravitational waves associated with the EMRI motion fall within the mHz regime, making them target sources for future space-based detectors. However, because of the crowded nature of these galactic centers, these EMRIs could be perturbed by other nearby orbiting bodies. In this work, we analyze potential perturbations in EMRIs due to a third-body perturber near resonance. We use the formalism and code tools developed in the previous paper in this series [Silva \& Hirata, {\slshape Phys. Rev. D} {\bfseries 106}:084508 (2022)] and expand them to account for a general outer body orbit, allowing for multiple resonant interactions within an orbit and across a variety of SMBH spins. We find that, after investigating nearly 142,000 resonant interactions across a restricted set of 180 different simulated orbit systems, none cause changes to the EMRI dynamics beyond a perturbative correction, but could lead to potentially large changes in the phase of the waveform of order 0.1 radian. Detectable phase changes in the waveform induced by third-body perturbers could be a common occurrence and will require careful consideration for developing accurate EMRI waveform models. This analysis suggests that our formalism and pipeline are robust enough to handle a wide variety of resonances from various perturbing orbit configurations around the EMRI, which will aid in developing more accurate waveform models to better probe galactic center environments and test theories of gravity using gravitational wave observations of EMRIs.

Heavy-tailed combination tests, such as the Cauchy combination test and harmonic mean p-value method, are widely used for testing global null hypotheses by aggregating dependent p-values. Existing theoretical guarantees, however, are largely restricted to the case of asymptotically independent p-values, leaving the behavior of these tests under broader dependence structures poorly understood. We develop a unified framework based on multivariate regularly varying copulas, a flexible class defined by a mild regularity condition on the joint behavior of p-values near zero, that accommodates a wide range of dependence structures. Within this framework, heavy-tailed combination tests are asymptotically valid when the transformation distribution has tail index $γ\leq 1$, with $γ= 1$ maximizing power while preserving validity. We further show that combination tests with $γ= 1$ achieve strictly greater asymptotic power than Bonferroni's method if and only if the p-values are not asymptotically independent and signals are not extremely sparse, with the power advantage growing as dependence strengthens. Bonferroni emerges as the $γ\to 0$ limit and becomes overly conservative under asymptotic dependence. These results provide theoretical support for using truncated Cauchy or Pareto combination tests, offering a principled approach to enhance power while controlling false positives under complex dependence.

Odd fluids are a class of fluids characterized by non-zero antisymmetric transport coefficient tensors induced by broken time-reversal symmetry. In our previous work, a mesoscale simulation model for two-dimensional isotropic odd fluids was developed. Here, we extend the model to the three-dimensional case that corresponds to an anisotropic odd fluid with cylindrical symmetry. Using kinetic theory, we analytically derive the viscosity tensor and Navier-Stokes equation for the three-dimensional mesoscale odd fluid, which are quantitatively verified by simulations. Furthermore, through both simulation and hydrodynamic theory, we demonstrate that the planar Poiseuille flow of the three-dimensional odd fluid exhibits exotic transport behavior. This work thus paves the way for performing large-scale simulations to explore and exploit intriguing phenomena of odd fluids.

Quantum algorithms provide a promising framework in high-energy physics, in particular, for unraveling the causal configurations of multiloop Feynman diagrams by identifying Feynman propagators with qubits, a challenge analogous to querying directed acyclic graphs in graph theory. In this paper, we present the Minimum Clique-optimised quantum Algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality. The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem. The evaluation of the MCA quantum algorithm is exhibited by analysing the transpiled quantum circuit depth and quantum circuit area.

This paper proposes a data-driven approach to designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for a class of single-input nonlinear systems with partially unknown dynamics, subject to both matched and unmatched disturbances. We first view the system as comprising two coupled dynamics, referred to as the upper and lower dynamics, with the last state serving as a virtual input to the upper dynamics. The proposed control-design methodology then follows a two-stage procedure: (i) designing a virtual state-feedback control law for the upper dynamics and (ii) synthesizing an ASSOSM controller for the full-order system. To this end, we collect noise-corrupted data from the system throughout a finite-time experiment. We then formulate a data-dependent condition, whose feasibility enables the design of a virtual state-feedback control law that renders the closed-loop upper dynamics input-to-state stable with respect to the unmatched disturbance. Building on this virtual state-feedback control law, we subsequently propose a data-driven nonlinear sliding variable, based on which an ASSOSM controller is designed for the full-order system. The state trajectories of the resulting closed-loop system are semiglobally ultimately bounded (S-GUB), with the ultimate bound explicitly depending on the magnitude of the unmatched disturbance. In particular, the control design parameters can be selected for any prescribed bounded set of initial conditions so that the state trajectories of the closed-loop system are S-GUB. Moreover, the effect of the matched disturbance is totally rejected after a finite time. The effectiveness of the proposed method is satisfactorily demonstrated in the simulation.

Time-Delay Interferometry (TDI) is essential for space-based gravitational wave (GW) missions, as it suppresses laser frequency noise and achieve the required sensitivity. Beyond the standard Michelson configuration, a variety of second-generation TDI schemes have been proposed, each utilizing different combinations of inter-spacecraft laser links. In this work, we conduct a comparative study of several representative TDI configurations with different time spans, and show that while their (quasi-)orthogonal channels are highly correlated, their performance in data analysis can differ among these schemes. In the low-frequency regime, the performance of different TDI configurations are nearly identical. Their distinctions emerge primarily at high frequencies, where the GW wavelength becomes comparable to the arm length. In this regime, shorter TDI time spans with minimal null frequencies facilitate more accurate waveform modeling and parameter recovery in frequency domain. In contrast, configurations with longer time spans and more null frequencies, such as the Michelson, are more susceptible to frequency aliasing and waveform modulation effects, which degrade inference accuracy. However, if signal modeling and analysis are performed in the time domain, the optimal science channels of these TDI configurations exhibit consistent performance in parameter inference. Considering the usability in both frequency and time domain, the short-span PD4L scheme, which exhibits minimal nulls and superior performance in high frequencies, emerges as a promising candidate for future space-based GW mission designs.

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive stepsize selections, the proposed methods generate stepsizes based on local curvature estimates, entirely eliminating the need for backtracking linesearch. A key tool in our analysis is a Bregman generalization of Young's inequality, which allows the control of a critical inner product in terms of the same Bregman distances used in the updates. Our theory applies to problems where the differentiable term is merely \emph{locally} smooth relative to a distance-generating function, without requiring the existence of global moduli or symmetry coefficients. Numerical experiments demonstrate their competitive performance compared to existing approaches across various problem classes.

Although computational phenotyping is a central informatics activity with resulting cohorts supporting a wide variety of applications, it is time-intensive because of manual data review. We previously assessed the ability of LLMs to perform computational phenotyping tasks using computable phenotypes for ARF respiratory support therapies. They successfully performed concept classification and classification of single-therapy phenotypes but underperformed on multi-therapy phenotypes. To understand issues with these complex tasks, we expanded PHEONA, a generalizable framework for evaluation of LLMs, to include methods specifically for evaluating faulty reasoning. We assessed the responses of two lightweight non-reasoning LLMs (Mistral Small 24 billion and Phi-4 14 billion) and one lightweight reasoning LLM (Qwen-distilled DeepSeek-r1 32 billion) both with and without prompt modifications to identify explanation correctness and unfaithfulness errors for phenotyping. For experiments without prompt modifications, both errors were present across all models. For experiments assessing accuracy impact after prompt modifications, Mistral had the highest overall accuracy impact when compared to DeepSeek and Phi. Since reasoning errors were ubiquitous across models, our enhancement of PHEONA to include a component for assessing faulty reasoning provides critical support for LLM evaluation and evidence for reasoning errors for complex tasks. While insights from reasoning errors can help prompt refinement, a deeper understanding of why LLM reasoning errors occur will likely require further development and refinement of interpretability methods.

Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten conjecture, then so is S. In this paper, we consider the dual situation where C is a cotilting right R-module, with S=End(C). We investigate the invariance of the property of satisfying the Auslander-Reiten conjecture when passing from R to S.

This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques on the data represented by the numerical solution of the initial-value problem at hand. The only assumption is that there are only a few terms that connects the components, so that the mathematical relations to be discovered are sparse in the set of possible functions. We illustrate the method through examples of applications.

We investigate the background cosmological expansion on the onset of cosmological homogeneous matter creation scenario, a dynamical dark matter approach ($w_{\rm dm} \neq 0$), and an alternative approach to both dark energy and modified gravity theories, after the recent DESI DR2-BAO release. We consider that the total matter sector consists of three independently evolving components, namely, radiation, baryons, and dark matter, with the latter being governed by an adiabatic matter creation process, affects the background homogeneously, leads to a modified continuity equation. Though the total stress-energy tensor is conserved the only violation of the conservation law in the dark matter sector is coming from the creation pressure, and under a proper choice of dark-matter particle creation rate one can obtain the present accelerating phase as well as the past thermal history of the Universe. We study two specific matter creation rates. By applying the dynamical-system analysis we show that both Model I and Model II can mimic a $Λ$CDM-like behavior. Furthermore, we perform a detailed observational confrontation using a series of latest observational datasets including Cosmic Chronometers (CC), Supernovae Type Ia (SNIa) (Pantheon+, DESY5 and Union3 samples) and DESI Baryon Acoustic Oscillations (BAO) (DR1 and DR2 samples). In both Model I and Model II we find evidence of matter creation at many standard deviations. Finally, applying the AIC and BIC information criteria we find that Model I is statistically equivalent with $Λ$CDM scenario, while Model II shows a mixed picture, namely for most datasets $Λ$CDM scenario is favoured, however when DESI data are included matter creation Model II is favoured over $Λ$CDM paradigm.

Flight in turbulence is constrained not only by aerodynamic efficiency, but also by how strongly flow disturbances are transmitted into unsteady loads and dynamic responses. Although disturbance rejection is typically attributed to active control, birds often sustain fixed-wing gliding in disturbed air, suggesting that the wing itself may passively attenuate aerodynamic perturbations. Here, we show that avian wings reduce aerodynamic sensitivity to incoming disturbances. Compared with a geometrically matched airfoil wing, the avian wing exhibits lower lift-response gain, smoother stall transition, reduced force fluctuations, and a broader operative angle-of-attack range across turbulence intensities. These wing-level properties translate into an expanded passive stability envelope in rigid-flyer dynamics. Flow diagnostics indicate that this robustness is associated with delayed separation and redistribution of turbulent kinetic energy, which suppress large-scale flow instability and weaken disturbance transmission. This passive robustness comes at the cost of reduced aerodynamic efficiency, revealing an efficiency-robustness trade-off in disturbed flows. Our results identify aerodynamic sensitivity and control demand as essential metrics for flight performance in turbulence, and suggest passive aerodynamic robustness as a design principle for resilient flying systems.

We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution results for values of $d$-tuples of elements of $\mathbb F_d$.

Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let $R$ denote the radius function defined on the base surface $S$. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on $S$ and their corresponding off-surface points, displaced along $R$-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of $S$. Moreover, our method mitigates the misalignment issues commonly seen in crust-based approaches through a lightweight fine-tuning procedure. We validate the accuracy and efficiency of OffsetCrust through extensive experiments, and demonstrate its practical utility in applications such as reconstructing original boundary surfaces from medial axis transform (MAT) representations.

In this paper we take the first steps towards the categorification of the Zelevinsky tensor product of finite dimensional representations of extended affine type A Hecke algebras.

In this paper, we give exact and asymptotic formulas for counting elliptic curves $ E_{A,B} \colon y^2 = x^3 + Ax + B $ with $ A, B \in \mathbb{Z} $, ordered by naive height. We study the family of all such curves and also several natural subfamilies, including those with fixed $ j $-invariant and those with complex multiplication (CM). In particular, we provide formulas for two commonly used normalizations of the naive height appearing in the literature: the calibrated naive height, defined by \[ H^{\mathrm{cal}}(E_{A,B}) := \max\{ 4|A|^3, 27B^2 \}, \] and the uncalibrated naive height, defined by \[ H^{\mathrm{ncal}}(E_{A,B}) := \max\{ |A|^3, B^2 \}. \] In fact, we prove our theorems with respect to the more general naive height $H_{α, β}(E_{A,B}) := \max\{ α|A|^3, βB^2 \}$, defined for arbitrary positive real numbers $α, β\in \mathbb{R}_{> 0}$. As part of our approach, we give a completely explicit parametrization of the set of curves $ E_{A,B} $ with fixed $ j $-invariant and bounded naive height, describing them as twists of the curve $ E_{A_j, B_j} $ of minimal naive height for the given $ j $-invariant. We also include tables comparing and verifying our theoretical predictions with exact counts obtained via exhaustive computer searches, and we compute data for CM elliptic curves of naive height up to $ 10^{30} $. Code in SageMath is provided to compute all exact and asymptotic formulas appearing in the paper.

Exploring quantum effects from black hole thermodynamics has always been a pivotal topic. In recent years, the free energy landscape and ensemble-averaged theory based on the Euclidean path integral approach have provided further understanding of the statistical aspects of the black hole system. We investigate the quantum-corrected thermodynamics of the Reissner-Nordstrom AdS black hole by including off-shell geometries in a reduced gravitational path integral. Within this collective-variable approximation, we derive an effective action by considering the subleading-order terms in the ensemble-averaged theory and show that the corresponding thermodynamic quantities define a consistent thermodynamics. Furthermore, the phase diagram was modified by the off-shell effects, resulting in a more abundant phase structure. We show that the traditional black hole thermodynamics can be recovered in the semi-classical limit. The region of first-order phase transitions shrinks and zero-order phase transitions emerge when off-shell effects are included. These results provide a tractable framework for understanding how off-shell black hole geometries generate quantum corrections to black hole phase structures.

The circumgalactic medium (CGM) plays a critical role in galaxy evolution, influencing gas flows, feedback processes, and galactic dynamics. Observations show a substantial cold gas reservoir in the CGM, but the mechanisms driving its formation and evolution remain unclear. Cosmic rays (CRs), as a source of non-thermal pressure, are increasingly recognized as key regulators of cold gas dynamics. This study explores how CRs affect cold clouds that condense from the hot CGM via thermal instability (TI). Using 3D CR-magnetohydrodynamic (CRMHD) simulations with AREPO, we assess the impact of various CR transport models on cold gas evolution. Under purely advective CR transport, CR pressure significantly suppresses the collapse of thermally unstable regions, altering the CGM's structure. In contrast, realistic CR transport models reveal that CRs escape collapsing regions via streaming and diffusion along magnetic fields, diminishing their influence on the thermal and dynamic structure of the cold CGM. The ratio of the CR escape time to the cloud collapse time emerges as a critical factor in determining the impact of CRs on TI. CRs remain confined within cold clouds when effective CR diffusion is slow which maximizes their pressure support and inhibits collapse. Fast effective CR diffusion, as realized in our 2-moment CRMHD model, facilitates rapid CR escape, reducing their stabilizing effect. This realistic CR transport model shows a wide dynamic range of the effective CR diffusion coefficient, ranging from $10^{29}$ to $10^{30}\,\mathrm{cm^{2}\,s^{-1}}$ for thermally- to CR-dominated atmospheres, respectively. In addition to these CR transport-related effects, we demonstrate that high numerical resolution is crucial to avoid spuriously large clouds formed in low-resolution simulations, which would result in overly long CR escape times and artificially amplified CR pressure support.

Wave scattering plays a central role for the modeling of complex wave propagation across all corners of science and engineering applications, including electromagnetic, acoustics, seismic and scattering physics. Wave control using time interfaces, where the properties of the medium through with the wave travels rapidly change in time, has opened further opportunities to control wave propagation in both space and time. For acoustic waves, studies on time modulated media have not been reported. In this context, full numerical solution of the wave equation using time interfaces is key to fully understand their potential. When applying time interfaces, the underlying physics of acoustic wave propagation and scattering and their similar roles on time and space, are still being explored. In this work, we introduce a mathematical formulation of the Lippmann-Schwinger integral equations for acoustic wave scattering when time interfaces are induced via a change of the velocity of the medium. We demonstrate that space-time duality for acoustic wave propagation with time interfaces and derive the Lippmann-Schwinger integral equations for wave scattering in time-dependent media, multiple scattering theory, Kirchhoff Helmholtz integrals, Green's functions, reciprocity theorems. We experimentally verify our theoretical derivation by studying and measuring the acoustic wave scattering in strongly scattering media. We illustrate the proposed framework and present results of acoustic wave scattering without prior knowledge of the background wave-fields. This improves the understanding of the generation and wave scattering and opens previously inaccessible research directions, potentially facilitating practical applications for acoustic, geophysical and optical imaging.

We invesigate the relation between projective and anomalous representations of categories, and show how to any anomaly $J\colon \mathcal{C}\to 2\mathrm{Vect}$ one can associate an extension $\mathcal{C}^J$ of $\mathcal{C}$ and a subcategory $\mathcal{C}^J_{\mathrm{ST}}$ of $\mathcal{C}^J$ with the property that: (i) anomalous representations of $\mathcal{C}$ with anomaly $J$ are equivalent to $\mathrm{Vect}$-linear functors $E\colon \mathcal{C}^J\to \mathrm{Vect}$, and (ii) these are in turn equivalent to linear representations of $\mathcal{C}^J_{\mathrm{ST}}$ where "$J$ acts as scalars". This construction, inspired by and generalizing the technique used to linearize anomalous functorial field theories in the physics literature, can be seen as a multi-object version of the classical relation between projective representations of a group $G$, with given $2$-cocycle $α$, and linear representations of the central extension $G^α$ of $G$ associated with $α$.

We extend Poonen's Bertini theorem over finite fields to Taylor conditions arising from locally free quotients of the sheaf of differentials on projective space. This is motivated by a result of Bilu and Howe in the motivic setting that allows for significantly more general Taylor conditions.

All living organisms use two universal genetic languages in their molecular biology machinery, one containing four nucleotide bases in its alphabet, and the other containing twenty amino acids in its alphabet. They can be understood as the optimal encodings of genetic information for the tasks they carry out, i.e. replication/transcription for DNA/RNA and translation for polypeptide chains. These tasks select needed letters of the alphabet by complementary nucleotide base-pairing, from a collection of molecules in the cell. The computer science paradigm for this process is database search; various algorithms for it can be constructed and compared according to number of attempts (or queries) they need to make to find the correct nucleotide base-pairing. Grover's search algorithm based on oscillatory wave dynamics perfectly fits the number of queries needed to search the genetic alphabets, and it is more efficient than the best Boolean search algorithm (i.e. binary tree search) that needs a larger number of queries. This result strongly suggests that the universal genetic languages have been selected by evolution as the optimal alphabets for the tasks they carry out, and are not an accident of history. The outstanding challenge is to demonstrate how Grover's search algorithm would be executed in vivo by the living organisms.

To fully understand the star formation process, we are compelled to study it in a variety of environments. Of particular interest are how star formation and the resulting initial mass function (IMF) vary as a function of metallicity. We have observed an embedded young cluster in Sh2-284 (hereafter S284), the HII region associated with the open cluster Dolidze 25 using JWST/NIRCam with the aim to study star formation in a metal-poor, i.e., about 1/3 of solar, environment. In particular, we aim to measure the peak of the IMF. Using JWST NIRCam photometry, we identified the embedded cluster S284-EC1 and resolved its low-mass content. By comparison with pre-main sequence evolutionary tracks we determine the mass and extinction for the individual cluster members. Extinction limited samples are created based on the distribution of extinction and the completeness of the data. For the region with a completeness of 50% or higher, we have fitted a log-normal distribution to the IMF. Adopting a fiducial age of 1 Myr of the members, the peak of the IMF is found to be at mc = 0.16+-0.02Msun, which is significantly smaller than the peak mass measured in local young clusters, such as mc = 0.26+0.11-0.07 Msun in the Orion Nebula Cluster (Gennaro & Robberto 2020), or the local Galactic disk value of mc = 0.25 Msun (Chabrier 2005). We have found evidence for IMF variation as a function of metallicity, i.e., the peak of the IMF shifts to lower masses as one goes from solar to 1/3 solar metallicity. However, we caution that the result is sensitive to the assumed age of the stellar population, i.e., with peak mass rising if an age older than 1 Myr is adopted. This study further motivates the need for expanded samples of low-metallicity regions and their content to enable more comprehensive measures of the IMF in such environments.

For $p>1$, we prove that, for a $p$-energy on a volume doubling metric measure space, the Poincaré inequality and the cutoff Sobolev inequality, both with $p$-walk dimension strictly larger than $p$, imply that the associated $p$-energy measure is singular with respect to the underlying measure. Under the slow volume regularity condition, we further prove that these two inequalities are equivalent to the resistance estimate; in particular, as part of the proof, we give a simple and direct derivation of the cutoff Sobolev inequality from the Poincaré inequality and the capacity upper bound. As a direct corollary, for a large family of fractals and metric measure spaces, including the Sierpiński gasket and the Sierpiński carpet, the $p$-energy measure is singular with respect to the underlying measure for any $p$ strictly greater than the Ahlfors regular conformal dimension.

The entry inhibitor Bulevirtide (BLV) was recently approved in Europe for treatment of chronic hepatitis D virus (HDV) infection, which is considered the most severe viral hepatitis infection. Theory indicates that models that account for free virus and infected cells, but do not include target cell dynamics (historically called the two-equation model) are limited to predicting a monophasic viral decline for antiviral agents that act only to block viral entry/infection. We investigated herein a recently published two-equation type model against clinical data obtained from patients with HDV treated with BLV monotherapy for up to 96 weeks using non-linear mixed effects modelling (NLME). We found that (i) although the model parameters had a relative standard error (RSE) <50\% suggesting that they were 'precisely estimated', the fits failed to reproduce the non-monophasic HDV kinetic patterns observed in most patients leading to incorrect predictions of the duration of treatment needed to reach a theoretical cure boundary, defined as less than 1 virion in the entire patient extracellular body fluid. (ii) The model cannot explain viral breakthrough, and (iii) the model wrongly predicts that viral load will remain at the same level once treatment is stopped. Lastly, we showed that including target cell dynamics in the model can explain not only monophasic viral decline during treatment but also non-monophasic HDV decline patterns such as biphasic, flat-partial response and viral breakthrough. Including target cell dynamics also predicts a viral rebound once BLV is stopped as observed in clinical studies.

The Generalized First Law (GFL) and the Generalized Second Law (GSL) of thermodynamics are studied for cosmological scenarios with spatial curvature through an apparent horizon. We focus on effective and alternative cosmic systems motivated by quantum cosmological models, where the entropy is considered a function of the apparent area, transforming the effective cosmological model into the standard form in cosmology. The general conditions for the validity of the GSL are analyzed for entropy as a general function of area and logarithmic corrections to the usual Black Hole entropy. The Weak Energy Condition (WEC) and the Strong Energy Condition (SEC) are implemented for the matter entropy part. In particular, we study the GFL and the regions where the GSL is valid for effective Loop Quantum Cosmology (LQC) models with spatial curvature $k=0,\pm 1$, taking every possible value of the logarithmic contributing factor for the entropy analysis. In addition, in order to solve some violations of the GSL, we explore the possibility of admitting negative absolute temperatures (NAT) in our system, where the validity conditions for an extended generalized second law (EGSL) are studied, and the time arrow from the second law is discussed for the LQC models.

We verify a construction which, for $\Bbb K$ the reals, complex numbers, quaternions, or octonions, builds a spherical $t$-design by placing a spherical $t$-design on each $\Bbb K$-projective or $\Bbb K$-Hopf fiber associated to the points of a $\lfloor t/2\rfloor$-design on a quotient projective space $\Bbb{KP}^n\neq\Bbb{OP}^2$ or sphere. This generalizes work of König and Kuperberg, who verified the $\Bbb K=\Bbb C$ case of the projective settings, and of Okuda, who (inspired by independent observation of this construction by Cohn, Conway, Elkies, and Kumar) verified the $\Bbb K=\Bbb C$ case of the generalized Hopf settings.

This paper introduces a causal machine learning approach to investigate the effects of free trade agreements and applies it to the EU-Canada Comprehensive Economic and Trade Agreement (CETA). Previous estimates of the impact of trade liberalization have been found to be unstable and contradictory, possibly due to the presence of heterogeneous treatment effects. The matrix completion estimator computes multidimensional counterfactuals in trade data at the firm, product, and destination levels. Compared with other estimators, it relies on a weaker exogeneity assumption and a more general functional form. In the case of CETA, we obtain both positive and negative idiosyncratic treatment effects at the product-destination level, although the sales-weighted average treatment effect is 6.4% in the year after the agreement. At the same time, we can estimate idiosyncratic treatment effects for the extensive margin at the product-destination level; thus, we find product churning beyond regular entry-exit dynamics: 8.1% that were not previously exported, and about 7.3% that are no longer exported. Finally, we consider the case of multiproduct firms after ranking product portfolios. After CETA, we observe a reallocation of French exports toward the first and most exported products, possibly driven by increased competition in the local market by other European producers after trade liberalization.