Partial Signatures and their Applications

We introduce Partial Signatures, where a signer, given a message, can compute a ``stub\u27\u27 which preserves her anonymity, yet later she, but nobody else, can complete the stub to a full and verifiable signature under her public key. We provide a formal definition requiring three properties, namely anonymity, unambiguity and unforgeability. We provide schemes meeting our definition both with and without random oracles. Our schemes are surprisingly cheap in both bandwidth and computation. We describe applications including anonymous bidding and betting

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level

Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Topological insulating (TI) phases were originally highlighted for their disorder-robust bulk responses, such as the quantized Hall conductivity of 2D Chern insulators. With the discovery of time-reversal- ($\mathcal{T}$-) invariant 2D TIs, and the recognition that their spin Hall conductivity is generically non-quantized, focus has since shifted to boundary states as signatures of 2D and 3D TIs and symmetry-enforced topological crystalline insulators (TCIs). However, in $\mathcal{T}$-invariant (helical) 3D TCIs such as bismuth, $\alpha$-BiBr, and MoTe$_2$-termed higher-order TCIs (HOTIs)-the boundary signatures manifest as 1D hinge states, whose configurations are dependent on sample details, and bulk signatures remain unknown. In this work, we introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetal states with gapless spin spectra, and $\mathcal{T}$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles $\theta^\pm = \pi$ indicative of a 3D spin-magnetoelectric bulk response. We provide experimental signatures of each spin-stable regime of helical HOTIs, including an extensive bulk spin Hall response in 3D QSHIs and half-quantized 2D TI states on the gapped surfaces of T-DAXIs originating from a partial parity anomaly. We use ab-initio calculations to compute the spin-resolved topology of candidate helical HOTIs, finding that $\beta$-MoTe$_2$ realizes a spin-Weyl state and that $\alpha$-BiBr hosts both 3D QSHI and T-DAXI regimes.Comment: v2: 19+141 pages, 8+44 figures. Expanded materials analysis, added detailed calculations of spin-resolved topology and spin Hall conductivity with applications to BiBr. 1 author added for help with additional analyses. Nested and spin-resolved Wilson loop code with example scripts and documentation freely available at https://github.com/kuansenlin/nested_and_spin_resolved_Wilson_loo

Weighted Pushdown Systems with Indexed Weight Domains

The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications. To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness