Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
The paper clusters PK curves using ML, finding it useful for identifying similar patterns.
problem Improving drug development and patient outcomes through ML in pharmacogenomics.
method Unsupervised clustering of PK curves using various dissimilarity measures.
result Euclidean distance is most suitable for clustering PK curves, and clustering can validate pharmacogenomic results.
Euclidean systems and real PK arrangements linked via geometry.
problem Establishing a connection between Euclidean systems and real PK arrangements.
method Proving a correspondence between Euclidean ∨-systems and real PK arrangements, and showing homeomorphism of moduli spaces. result Moduli space of Euclidean ∨-systems is homeomorphic to a polytope's interior, and hyperplane arrangements are simplicial. The study finds PK cone metrics on complex manifolds near hyperplane arrangements.
problem Finding metrics on complex manifolds near singularities.
method Analyzing flat torsion-free meromorphic connections on \(\mathbb{C}^n\) with simple poles at hyperplanes.
result Metric completion of certain connections yields PK cone metrics on \(\mathbb{C}^n\).
We consider higher dimensional generalisations of normal almost contact structures, the so called f.pk-structures where parallelism spans a Lie algebra g (f.pk-g-structures). Two types of these structures are discussed. In the first case, we construct an almost complex structure on a product manifold mirroring K-struct…
Locally private mechanisms' output divergence bounds derived.
problem Bounding divergence between locally private mechanisms' outputs.
method Sharp upper bounds on divergence between input and output distributions.
result Established locally private versions of estimation risk bounds.
Proves mapping class group of nonorientable surfaces can be generated by three torsions.
problem Generates mapping class group of nonorientable surfaces by three torsions.
method Proves using algebraic methods and properties of nonorientable surfaces.
result Proves mapping class group of nonorientable surfaces can be generated by three torsions.
Physics-Informed Neural Networks (PINNs) benchmarked against clinical estimator and reveal parameter identifiability
problem Chemotherapy pharmacokinetics (PK) with tissue concentration not measured
method Physics-Informed Neural Networks (PINNs) benchmarked against clinical estimator and reveal parameter identifiability
result PINN recovers tissue concentration and identifies non-identifiable parameters
We show that if K is an L-space twisted torus knot Tp,pk±1l,m with p≥2, k≥1, m≥1 and 1≤l≤p−1, then the fundamental group of the 3-manifold obtained by sr-surgery along K is not left-orderable whenever sr≥2g(K)−1, where g(K) is the genus of K.
Efficient knockoffs for large-scale feature selection.
problem Large-scale feature selection problems.
method Gaussian model-X knockoffs with efficient methods for solving semidefinite programs.
result Efficient knockoffs can be generated with linear complexity in the dimension.
The paper calculates bounds for unknotting rational tangles using knot Floer homology.
problem Calculating the minimum number of rational replacements to unknot a tangle.
method From the link Floer complex, extract a lower bound for the rational unknotting number using knot Floer homology.
result The torsion obstruction is a lower bound for the proper rational unknotting number.
New methods tackle statistical inverse problems with random data.
problem Statistical inverse problems with random experimental design.
method Spectral regularization, regularization by projection, convex penalties.
result Minimax rates in expectation and probability for convergence.
Let X be a compact Kahler orbifold without \C-codimension-1 singularities. Let D be a suborbifold divisor in X such that D \supset Sing(X) and -pK_X = q[D] for some p, q \in \N with q > p. Assume that D is Fano. We prove the following two main results. (1) If D is Kahler-Einstein, then, applying results from our previo…
Motivation: A major challenge in the development of machine learning based methods in computational biology is that data may not be accurately labeled due to the time and resources required for experimentally annotating properties of proteins and DNA sequences. Standard supervised learning algorithms assume accurate in…
Detection of protein-protein interactions (PPIs) plays a vital role in molecular biology. Particularly, infections are caused by the interactions of host and pathogen proteins. It is important to identify host-pathogen interactions (HPIs) to discover new drugs to counter infectious diseases. Conventional wet lab PPI pr…
Paper finds exact recovery threshold in general hypergraph model.
problem Exact recovery of communities in general hypergraph model.
method Developed a two-stage polynomial-time algorithm for exact recovery.
result Sharp threshold for exact recovery in terms of generalized Chernoff-Hellinger divergence.
A new stable similarity measure for time series using persistent homology.
problem Constructing a robust measure of time series similarity.
method Persistent homology for stability, bi-conditional periodicity score for similarity.
result Stability of the bi-conditional periodicity score under perturbations and dimension reduction.