Department of MathematicsEach 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 »
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 »
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 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 »
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 »
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 »
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 »
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 »
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 »
We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach… read more about this publication »
The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously… read more about this publication »
We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper and lower tails of homomorphism counts in the r-uniform… read more about this publication »
Sum-of-norms clustering is a popular convexification of $K$-means clustering. We show that, if the dataset is made of a large number of independent random variables distributed according to the uniform measure on the union of two disjoint balls of unit radius, and if the balls are sufficiently… read more about this publication »
We study the existence of weak solutions to the p-Navier-Stokes equations with a symmetric p-Laplacian on bounded domains. We construct a particular Schauder basis in W01, p(Ω) with divergence free constraint and prove existence of weak solutions using the Galerkin approximation via this basis.… read more about this publication »
We consider a generalization of local density of states which is “windowed” with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual LDOS is recovered in the limit where the position window… read more about this publication »
Objective.We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one higher quality EDR signal.Methods.We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality… read more about this publication »
We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in the conventional fashion as an exponential of an… read more about this publication »
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate polynomial expressions in homomorphism densities on kernels W,… read more about this publication »
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that many established in vivo measurements of protein dynamics… read more about this publication »