The derived category of surface algebras: the case of the torus with one boundary component

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily computable derived invariant for such surface algebras. This result permits to give answers to open questions on gentle algebras: it provides examples of gentle algebras with the same AG-invariant (in the sense of Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial positive answer to a conjecture due to Bobi\'nski and Malicki on gentle $2$-cycles algebras.Comment: 22 pages, a mistake concerning the computation of the mapping class group has been fixed, version 3: 25 pages, to appear in Algebras and Representation Theor

Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Associative learning in the cnidarian Nematostella vectensis.

The ability to learn and form memories allows animals to adapt their behavior based on previous experiences. Associative learning, the process through which organisms learn about the relationship between two distinct events, has been extensively studied in various animal taxa. However, the existence of associative learning, prior to the emergence of centralized nervous systems in bilaterian animals, remains unclear. Cnidarians such as sea anemones or jellyfish possess a nerve net, which lacks centralization. As the sister group to bilaterians, they are particularly well suited for studying the evolution of nervous system functions. Here, we probe the capacity of the starlet sea anemone Nematostella vectensis to form associative memories by using a classical conditioning approach. We developed a protocol combining light as the conditioned stimulus with an electric shock as the aversive unconditioned stimulus. After repetitive training, animals exhibited a conditioned response to light alone indicating that they learned the association. In contrast, all control conditions did not form associative memories. Besides shedding light on an aspect of cnidarian behavior, these results root associative learning before the emergence of NS centralization in the metazoan lineage and raise fundamental questions about the origin and evolution of cognition in brainless animals

Multiple wavelengths reflectance microscopy to study the multi-physical behavior of MEMS

International audienceIn order to characterize surface chemomechanical driving micro-electro-mechanical systems (MEMS) behavior, we propose herein a method to simultaneously obtain a full kinematic field describing the surface displacement and a map of its chemical modification from optical measurements. Using a microscope, reflected intensity fields are recorded for two different illumination wavelengths. Decoupling the wavelength-independent and -dependent contributions to the measured relative intensity changes then yields the sought fields. This method is applied to the investigation of the electro-elastic coupling, providing images of both the local surface electrical charge density and the device deformation field

Shall We (Math and) Dance?

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance.Comment: preprin

Development of a Passive and Slope Adaptable Prosthetic Foot

Historically, users of prosthetic ankles have relied on actively operated systems to provide effective slope adaptability. However, there are many drawbacks to these systems. This research builds upon work previously completed by Hansen et al. as it develops a passive, hydraulically operated prosthetic ankle with the capability of adapting to varying terrain in every step. Using gait cycle data and an analysis of ground reaction forces, the team determined that weight activation was the most effective way to activate the hydraulic circuit. Evaluations of the system pressure and energy showed that although the spring damper system results in a loss of 9J of energy to the user, the footplate stores 34J more than a standard prosthesis. Therefore, the hydraulic prosthetic provides a 54% increase in stored energy when compared to a standard prosthesis. The hydraulic circuit manifold prototype was manufactured and tested. Through proof of concept testing, the prototype proved to be slope adaptable by successfully achieving a plantarflexion angle of 16 degrees greater than a standard prosthetic foot currently available on the market.Massachusetts Institute of Technology. Tata Center for Technology and Desig

Управління виробничими запасами на підприємстві (на матеріалах ПрАТ «Детвілер Ущільнюючі Технології України»)

. The second-order matching problem is the problem of determining, for a finite set {#t i , s i # | i # I} of pairs of a second-order term t i and a first-order closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I . It is well-known that the second-order matching problem is NP-complete. In this paper, we introduce the following restrictions of a matching expression: k-ary, k-fv , predicate, ground , and function-free. Then, we show that the second-order matching problem is NP-complete for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching expressions, while it is solvable in polynomial time for a binary function-free predicate, a unary function-free, a k-fv function-free (k # 0), and a ground predicate matching expressions. 1 Introduction The unification problem is the problem of determining whether or not any two ter..

Theoretical overview of atomic parity violation. Recent developments and challenges

Recent advances in interpreting the most accurate to-date measurement of atomic parity violation in Cs are reviewed. The inferred nuclear weak charge, Q_W = - 72.65(28)_expt (36)_theor, agrees with the prediction of the standard model at 1 sigma level. Further improved interpretation is limited by an accuracy of solving basic correlation problem of atomic structure. We report on our progress in solving this problem within the relativistic coupled-cluster formalism. We include single-, double- and triple- electronic excitations in the coupled-cluster expansion. Numerical results for energies, electric-dipole matrix elements, and hyperfine-structure constants of Cs are presented.Comment: PAVI'06 proceedings + EJPA; refs + SM Qw fixe

Being a droog vs. being a friend: A qualitative investigation of friendship models in Russia vs. Canada

Introduction. A substantial body of work has established that friendship is an important non-kin interpersonal relationship, with many positive outcomes. An issue with this literature is that it originated primarily in anglocentric Euro-American societies, when several studies have shown that the meaning of friendship varies across cultural settings. In particular, linguistic analyses advance that the meaning of friendship in Russian is quite different from that in English. The goal of this study was to seek psychological evidence of these linguistic findings by documenting similarities and differences in people’s understanding of friendship in both cultural contexts. Methods. The research consisted of a qualitative investigation of friendship cultural models among Russian migrants to Canada, through semi-structured interviews that were analysed using an inductive thematic analysis, whereby data segments are coded and codes are gradually refined and streamlined in order to identify the main themes that emerge from the data. Results. Participants’ depictions of friendship in Russian vs. Canadian contexts were largely in line with semantic analyses of friendship in Russian vs. English, with friendship being described as a stronger and deeper bond, but also more demanding in Russia than in Canada. Discussion. The findings support Wierzbicka’s proposal that key terms in a language encapsulate cultural models prevalent among its speakers. The results are also consistent with the existence of close parallels between people’s cultural models and the linguistic ecologies in which they live