In this paper, we investigate the instability of growing tumors by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al. (Z Angew Math Phys 74:107, 2023). Building upon the insights derived from… read more about this publication »
The accurate quantification of symmetry is a key goal in biological inquiries because symmetry can affect biological performance and can reveal insights into development and evolutionary history. Recently, we proposed a versatile measure of symmetry, transformation information (TI), which provides… read more about this publication »
We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdoba-Córdoba-Fontelos (CCF) equation. We… read more about this publication »
We consider the advection-diffusion equation on T2 with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale |log υ|, where υ is the diffusivity parameter. This is the optimal decay rate as υ → 0 for… read more about this publication »
We provide a classification of curvature homogeneous hypersurfaces in space forms by classifying the ones in and . In higher dimensions, besides the isoparametric and the constant curvature ones, there is a single one in . Besides the obvious examples, we show that there exists an isolated… read more about this publication »
MotivationFeature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery control, or (iii) identify few true positives.… read more about this publication »
We consider the patch problem for the (Formula presented.) -(surface quasi-geostrophic) SQG system with the values (Formula presented.) and (Formula presented.) being the 2D Euler and the SQG equations respectively. It is well-known that the Euler patches are globally wellposed in non-endpoint… read more about this publication »
We prove a uniqueness result for asymptotically conical (AC) gradient shrinking solitons for the Laplacian flow of closed G2-structures: If two gradient shrinking solitons to Laplacian flow are asymptotic to the same closed G2-cone, then their G2-structures are equivalent, and in particular, the… read more about this publication »
Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS… read more about this publication »
We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key novelty in the formula is that all “boundary terms” are given either by constants or sums over smaller quadrics related to… read more about this publication »
Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose… read more about this publication »
The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be used to find parametrizations of the moduli. One application… read more about this publication »
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial description as a sum over lattice paths in Zn of… read more about this publication »
We study the relation between the coregularity, the index of log Calabi-Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi-Yau pair of coregularity is at most, where is the Weil index of. This extends a recent result due to Filipazzi, Mauri and Moraga. We prove… read more about this publication »
The Homomorphism Preservation Theorem (HPT) of classical model theory states that a first-order sentence is preserved under homomorphisms if, and only if, it is equivalent to an existential-positive sentence. This theorem remains valid when restricted to finite structures, as demonstrated by the… read more about this publication »
In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for… read more about this publication »
We consider steady states of the two-dimensional incompressible Euler equations on T2 and construct smooth and singular steady states around a particular singular steady state. More precisely, we construct families of smooth and singular steady solutions that converge to the Bahouri–Chemin patch. read more about this publication »
We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary masses can be exchanged between the particles. We derive a… read more about this publication »
Single-cell RNA sequencing has been widely used to investigate cell state transitions and gene dynamics of biological processes. Current strategies to infer the sequential dynamics of genes in a process typically rely on constructing cell pseudotime through cell trajectory inference. However, the… read more about this publication »
Known as the no fast-forwarding theorem in quantum computing (see, e.g., Theorem 3 in [D. W. Berry et al., Comm. Math. Phys., 270 (2007), pp. 359-371], Theorem 5 in [A. M. Childs, Comm. Math. Phys., 294 (2010), pp. 581-603], and [R. Kothari, Efficient Simulation of Hamiltonians, M.S. thesis,… read more about this publication »
We study Betti numbers of sequences of Riemannian manifolds which Benjamini–Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we derive two distinct convergence results. First, under a negative Ricci curvature assumption and no assumption on sign of… read more about this publication »
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can also overcome the non-physical issues that arise from many… read more about this publication »
We show that the Euclidean 3-space R3 is stable for the Positive Mass Theorem in the following sense. Let (Mi,gi) be a sequence of complete asymptotically flat 3-manifolds with nonnegative scalar curvature and suppose that the ADM mass m(gi) of one end of Mi converges to 0. Then for all i, there is… read more about this publication »
We consider nonnegative solutions of the quasilinear heat equation in one dimension. Our solutions may vanish and may be unbounded. The equation is then degenerate, and weak solutions are generally nonunique. We introduce a notion of strong solution that ensures uniqueness. For suitable initial… read more about this publication »