Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module

Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We compare their asymptotic complexity to that of previous algorithms given by Gekeler, Narayanan and Garai-Papikian and discuss their practical behavior. In particular, we find that all three approaches represent either an improvement in complexity or an expansion of the parameter space over which the algorithm may be applied. Some experimental results are also presented

The use of self-report measures to examine changes in perception in response to fittings using different signal processing parameters

Clinicians have long used self-report methods to assess hearing aid benefit. However, there are fewer data as to whether self-report instruments can be used to compare differences between signal processing settings. This study examined how self-perceived performance varied as a function of modifications in signal processing using two self-report measures. Data were collected as part of a double-blind randomised crossover clinical trial. Participants were fit with two fittings: mild processing (slow time constants, disabled frequency lowering) and strong processing (fast time constants, frequency lowering enabled). The speech, spatial, and qualities of hearing (SSQ) questionnaire and the Effectiveness of Auditory Rehabilitation (EAR) questionnaire were collected at multiple time points. Older adults with sensorineural hearing loss who had not used hearing aids within the previous year participated (49 older adults were consented; 40 were included in the final data analyses). Findings show that listeners report a difference in perceived performance when hearing aid features are modified. Both self-report measures were able to capture this change in perceived performance. Self-report measures provide a tool for capturing changes in perceived performance when hearing aid processing features are modified and may enhance provision of an evidence-based hearing aid fitting

A faster pseudo-primality test

We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.Comment: Published in Rendiconti del Circolo Matematico di Palermo Journal, Springe

Boundary layer models for calving marine outlet glaciers

We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. Stable steady states can then have grounding lines located on retrograde slopes. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier and to the specifics of the calving law used

Computing the endomorphism ring of an ordinary elliptic curve over a finite field

We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field F_q. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q, while our bound for the second algorithm depends primarily on log |D_E|, where D_E is the discriminant of the order isomorphic to End(E). As a byproduct, our method yields a short certificate that may be used to verify that the endomorphism ring is as claimed.Comment: 16 pages (minor edits

Multiple feedback loops through cytokinin signaling control stem cell number within the Arabidopsis shoot meristem

A central unanswered question in stem cell biology, both in plants and in animals, is how the spatial organization of stem cell niches are maintained as cells move through them. We address this question for the shoot apical meristem (SAM) which harbors pluripotent stem cells responsible for growth of above-ground tissues in flowering plants. We find that localized perception of the plant hormone cytokinin establishes a spatial domain in which cell fate is respecified through induction of the master regulator WUSCHEL as cells are displaced during growth. Cytokinin-induced WUSCHEL expression occurs through both CLAVATA-dependent and CLAVATA-independent pathways. Computational analysis shows that feedback between cytokinin response and genetic regulators predicts their relative patterning, which we confirm experimentally. Our results also may explain how increasing cytokinin concentration leads to the first steps in reestablishing the shoot stem cell niche in vitro

On the shortness of vectors to be found by the Ideal-SVP quantum algorithm

The hardness of finding short vectors in ideals of cyclotomic number fields (hereafter, Ideal-SVP) can serve as a worst-case assumption for numerous efficient cryptosystems, via the average-case problems Ring-SIS and Ring-LWE. For a while, it could be assumed the Ideal-SVP problem was as hard a

Numerical analysis and simulation of the dynamics of mountain glaciers

In this chapter, we analyze and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solutions are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice, which describes the time evolution of a glacier. The accumulation due to snow precipitation and melting are accounted for in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a two-grids method. As an illustration, we simulate the evolution of Aletsch glacier, Switzerland, over the 21st century by using realistic climatic conditions

Surgical Repair of a Sinus of Valsalva Aneurysm

A surgically challenging case of an unruptured Sinus of Valsalva aneurysm (SoVA) with severe aortic regurgitation (AR) due to cusp prolapse is presented. Sinus reconstruction with a patch cut out from the sinus portion of a Gelweave Valsalva graft (Terumo Vascutek) was performed. Intraoperative measurements showed insufficient effective height of the right coronary cusp; therefore, cusp plication and pericardial patch augmentation of the right coronary cusp were performed with satisfying result