For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled invariant measures and study how they change as the velocity… read more about this publication »

We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean square error ϵ using O(1/ϵ) total evolution time, which is… read more about this publication »

We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method or form of NEUS. We prove the convergence of the method under certain assumptions, with expressions for the convergence… read more about this publication »

We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to establish a number of results that reveal a form of… read more about this publication »

We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by (y,Q(y))⊆Rn+1, for an arbitrary non-degenerate quadratic form Q, admits an a priori bound on Lp for all 1 read more about this publication »

In this paper, we show that the Keller-Segel equation equipped with zero Dirichlet Boundary condition and actively coupled to a Stokes-Boussinesq flow is globally well-posed provided that the coupling is sufficiently large. We will in fact show that the dynamics is quenched after certain time. In… read more about this publication »

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The… read more about this publication »

Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in… read more about this publication »

Each element of (Z≥0)2 is realized as the Hodge vector (h3,0(Z), h2,1(Z)) of some compact, connected, three dimensional, complex, submanifold, Z ⊂ PNC . Each (x, y) ∈ (Z≥1)2 with y ≤ 11x + 8 is shown to be the Hodge vector of a projective desingularized fiber product of elliptic surfaces which… read more about this publication »

We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral equation when one surface is close to another or to obtain… read more about this publication »

For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to 0) if and only if its Fermi projector admits an orthogonal basis with finite second moment (i.e., all basis elements satisfy ∫|x|2|w(x)|2dx<∞). In… read more about this publication »

The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins… read more about this publication »

RATIONALE AND OBJECTIVES: To determine the imaging changes and their associated positive predictive value (PPV) for invasive breast cancer in women undergoing active monitoring for ductal carcinoma in situ (DCIS). MATERIALS AND METHODS: In this seven-year follow-up retrospective IRB-exempted cohort… read more about this publication »

We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on graphs induced by finite-state reversible continuous time… read more about this publication »

We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn–Hilliard models with variable mobility. These splitting methods incorporate a linear, constant coefficient implicit step,… read more about this publication »

Selective serotonin reuptake inhibitors (SSRIs) are widely used for depression based on the monoamine deficiency hypothesis. However, the clinical use of these agents is controversial, in part because of their variable clinical efficacy and in part because of their delayed onset of action. Because… read more about this publication »

Information about the absolute Galois group GK of a number field K is encoded in how it acts on the étale fundamental group π of a curve X defined over K. In the case that K = ℚ(ζn) is the cyclotomic field and X is the Fermat curve of degree n ≥ 3, Anderson determined the action of GK on the étale… read more about this publication »

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles’ positions in the combined limit as the number of particles grow to infinity and the time-… read more about this publication »

We consider general exponential random graph models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs Fk. Whereas previous work has shown a degeneracy phenomenon in dense ERGMs, we show this can be cured by raising the sufficient… read more about this publication »

SifiNet is a robust and accurate computational pipeline for identifying distinct gene sets, extracting and annotating cellular subpopulations, and elucidating intrinsic relationships among these subpopulations. Uniquely, SifiNet bypasses the cell clustering stage, commonly integrated into other… read more about this publication »

The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the boundary vorticity can be determined via the dynamical equation up to bounded errors for… read more about this publication »

BACKGROUND: Delta radiomics is a high-throughput computational technique used to describe quantitative changes in serial, time-series imaging by considering the relative change in radiomic features of images extracted at two distinct time points. Recent work has demonstrated a lack of prognostic… read more about this publication »