scholarly journals On the -invariant of the cyclotomic derivative of a Katzp-adic -function

2014 ◽  
Vol 14 (1) ◽  
pp. 131-148 ◽  
Author(s):  
Ashay A. Burungale
Keyword(s):  
Modular Form ◽  
Recent Work ◽  
Crucial Role ◽  
Root Number ◽  
Main Conjecture ◽  
Ideal Approach ◽  
Eisenstein Ideal

AbstractWhen the branch character has root number$- 1$, the corresponding anticyclotomic Katz$p$-adic$L$-function vanishes identically. For this case, we determine the$\mu $-invariant of the cyclotomic derivative of the Katz$p$-adic$L$-function. The result proves, as an application, the non-vanishing of the anticyclotomic regulator of a self-dual CM modular form with root number$- 1$. The result also plays a crucial role in the recent work of Hsieh on the Eisenstein ideal approach to a one-sided divisibility of the CM main conjecture.

scholarly journals Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms

2018 ◽  
Vol 30 (4) ◽  
pp. 887-913 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Main Conjecture ◽  
Elliptic Modular Form

Abstract This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic {\mathbb{Z}_{p}} -tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson–Flach elements.

scholarly journals The Key Role of Epigenetics in the Persistence of Asexual Lineages

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Emilie Castonguay ◽  
Bernard Angers
Keyword(s):  
Phenotypic Plasticity ◽  
Recent Work ◽  
Molecular Mechanism ◽  
Crucial Role ◽  
Environmental Variation ◽  
Epigenetic Modifications ◽  
Epigenetic Variation ◽  
Epigenetic Mechanisms ◽  
Evolutionary Persistence

Asexual organisms, often perceived as evolutionary dead ends, can be long-lived and geographically widespread. We propose that epigenetic mechanisms could play a crucial role in the evolutionary persistence of these lineages. Genetically identical organisms could rely on phenotypic plasticity to face environmental variation. Epigenetic modifications could be the molecular mechanism enabling such phenotypic plasticity; they can be influenced by the environment and act at shorter timescales than mutation. Recent work on the asexual vertebrate Chrosomus eos-neogaeus (Pisces: Cyprinidae) provides broad insights into the contribution of epigenetics in genetically identical individuals. We discuss the extension of these results to other asexual organisms, in particular those resulting from interspecific hybridizations. We finally develop on the evolutionary relevance of epigenetic variation in the context of heritability.

scholarly journals Dissections of a "strange" function

2015 ◽  
Vol 11 (05) ◽  
pp. 1557-1562 ◽  
Author(s):  
Scott Ahlgren ◽  
Byungchan Kim
Keyword(s):  
Modular Form ◽  
Recent Work ◽  
Generating Function ◽  
Prime Power ◽  
Partial Sums ◽  
Root Of Unity ◽  
Prime Modulus

The "strange" function of Kontsevich and Zagier is defined by [Formula: see text] This series is defined only when q is a root of unity, and provides an example of what Zagier has called a "quantum modular form". In their recent work on congruences for the Fishburn numbers ξ(n) (whose generating function is F(1 - q)), Andrews and Sellers recorded a speculation about the polynomials which appear in the dissections of the partial sums of F(q). We prove that a more general form of their speculation is true. The congruences of Andrews–Sellers were generalized by Garvan in the case of prime modulus, and by Straub in the case of prime power modulus. As a corollary of our theorem, we reprove the known congruences for ξ(n) modulo prime powers.

scholarly journals Unitary cycles on Shimura curves and the Shimura lift II

2014 ◽  
Vol 150 (12) ◽  
pp. 1963-2002
Author(s):  
Siddarth Sankaran
Keyword(s):  
Modular Form ◽  
Recent Work ◽  
Chow Groups ◽  
Shimura Varieties ◽  
Shimura Curves ◽  
Shimura Lift ◽  
Generating Series

AbstractWe consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these divisors in a formal generating series, one obtains the$q$-expansion of a modular form of weight 3/2. The present work concerns the Shimura lift of this modular form: we identify the Shimura lift with a generating series comprising divisors arising in the recent work of Kudla and Rapoport regarding cycles on Shimura varieties of unitary type. In the prequel to this paper, the author considered the geometry of the two families of cycles. These results are combined with the Archimedean calculations found in this work in order to establish the theorem. In particular, we obtain new examples of modular generating series whose coefficients lie in arithmetic Chow groups of Shimura varieties.

scholarly journals The structure of helical lipoprotein lipase reveals an unexpected twist in lipase storage

2020 ◽  
Vol 117 (19) ◽  
pp. 10254-10264
Author(s):  
Kathryn H. Gunn ◽  
Benjamin S. Roberts ◽  
Fengbin Wang ◽  
Joshua D. Strauss ◽  
Mario J. Borgnia ◽  
...  
Keyword(s):  
Recent Work ◽  
Lipoprotein Lipase ◽  
Human Body ◽  
Crucial Role ◽  
Fluorescent Microscopy ◽  
Heparin Binding ◽  
Helix Formation ◽  
Intracellular Vesicles ◽  
Shed Light

Lipases are enzymes necessary for the proper distribution and utilization of lipids in the human body. Lipoprotein lipase (LPL) is active in capillaries, where it plays a crucial role in preventing dyslipidemia by hydrolyzing triglycerides from packaged lipoproteins. Thirty years ago, the existence of a condensed and inactive LPL oligomer was proposed. Although recent work has shed light on the structure of the LPL monomer, the inactive oligomer remained opaque. Here we present a cryo-EM reconstruction of a helical LPL oligomer at 3.8-Å resolution. Helix formation is concentration-dependent, and helices are composed of inactive dihedral LPL dimers. Heparin binding stabilizes LPL helices, and the presence of substrate triggers helix disassembly. Superresolution fluorescent microscopy of endogenous LPL revealed that LPL adopts a filament-like distribution in vesicles. Mutation of one of the helical LPL interaction interfaces causes loss of the filament-like distribution. Taken together, this suggests that LPL is condensed into its inactive helical form for storage in intracellular vesicles.

scholarly journals ON THE VANISHING OF FOURIER COEFFICIENTS OF CERTAIN GENUS ZERO NEWFORMS

2011 ◽  
Vol 07 (05) ◽  
pp. 1229-1245
Author(s):  
MATTHEW BOYLAN ◽  
SHARON ANNE GARTHWAITE ◽  
JOHN WEBB
Keyword(s):  
Modular Form ◽  
Recent Work ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Basic Question ◽  
Genus Zero ◽  
Similar Criterion

Given a classical modular form f(z), a basic question is whether any of its Fourier coefficients vanish. This question remains open for certain modular forms. For example, let Δ(z) = ΣΓ(n)qn ∈ S12(Γ0(1)). A well-known conjecture of Lehmer asserts that τ(n) ≠ 0 for all n. In recent work, Ono constructed a family of polynomials An(x) ∈ ℚ[x] with the property that τ(n) vanishes if and only if An(0) and An(1728) do. In this paper, we establish a similar criterion for the vanishing of coefficients of certain newforms on genus zero groups of prime level.

scholarly journals JALT2015 Conference Article: On Emotions in Foreign Language Learning and Use

2015 ◽  
Vol 39 (3) ◽  
pp. 13 ◽  
Author(s):  
Jean-Marc Dewaele
Keyword(s):  
Foreign Language ◽  
Language Learning ◽  
Recent Work ◽  
Learning Process ◽  
Crucial Role ◽  
Foreign Language Learning ◽  
Language Anxiety ◽  
Foreign Language Anxiety ◽  
Language Classroom

Emotions are at the heart of the foreign language learning process. Without emotion, boredom would reign and very little learning would take place. I report on some recent work that has investigated the role of emotion in the foreign language classroom, both positive (foreign language enjoyment) and negatives ones (foreign language anxiety). It seems that both learners and teachers play a crucial role in managing emotions in the classroom. I also report on the difficulties associated with the communication of emotions in a foreign language and on their relative absence in foreign language course books and during classes. This leaves learners ill-prepared to recognise and express emotions appropriately in a foreign language, which is an essential part of sociopragmatic competence. 外国語学習過程の中心には「感情」がある。感情がなければ飽きるのも早く、学びも限られてしまう。本論では、外国語の授業で感情が果たす肯定的な（例：外国語学習の楽しみ）および否定的な（例：外国語学習不安）役割について報告する。そして最近の研究を基に、いかに学習者と教員双方がクラスでの感情のコントロールに深くかかわっているかを考察する。また、外国語で感情を伝えることの難しさについても触れ、外国語の教科書や授業で感情表現が扱われることの少なさが、社会語用論的能力の主な要素である感情表現の理解不足につながっていることを指摘する。

scholarly journals Extreme Subjectivity

2019 ◽  
Vol 19 ◽  
Author(s):  
Brigitta Gyimesi
Keyword(s):  
Recent Work ◽  
Crucial Role ◽  
Point Of View ◽  
First Person ◽  
Cognitive Sciences ◽  
Person Perspective ◽  
Unnatural Narratology ◽  
Per Se ◽  
First Person Perspective ◽  
The Moment

The majority of narratives assign death scenes a crucial role in the development of the plot and characters; yet despite its prominence, dying per se frequently remains untold, with works utilising first-person narrators or focalisers proving especially problematic. From a commonsensical point of view, the authors’reluctance at representing the moment of deathis justifiable since they do not possess any comparable experience. But the fact that all first-person descriptions of death are inauthentic does not mean that they cannot be subject to narrative representation. As it will be demonstrated through the discussion of some recent work in the field of ‘unnatural narratology’ and the cognitive sciences, it may be possible to create a valid and valuable narrative of death even from a first-person perspective.

scholarly journals Congruences with Eisenstein series and -invariants

2019 ◽  
Vol 155 (5) ◽  
pp. 863-901 ◽  
Author(s):  
Joël Bellaïche ◽  
Robert Pollack
Keyword(s):  
Lower Bound ◽  
Zeta Function ◽  
Eisenstein Series ◽  
Galois Representations ◽  
Selmer Groups ◽  
Main Conjecture ◽  
The Family ◽  
Eisenstein Ideal ◽  
Hida Families

We study the variation of $\unicode[STIX]{x1D707}$-invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the $p$-adic zeta function. This lower bound forces these $\unicode[STIX]{x1D707}$-invariants to be unbounded along the family, and we conjecture that this lower bound is an equality. When $U_{p}-1$ generates the cuspidal Eisenstein ideal, we establish this conjecture and further prove that the $p$-adic $L$-function is simply a power of $p$ up to a unit (i.e. $\unicode[STIX]{x1D706}=0$). On the algebraic side, we prove analogous statements for the associated Selmer groups which, in particular, establishes the main conjecture for such forms.

scholarly journals CDKs in Sarcoma: Mediators of Disease and Emerging Therapeutic Targets

2020 ◽  
Vol 21 (8) ◽  
pp. 3018 ◽  
Author(s):  
Jordan L Kohlmeyer ◽  
David J Gordon ◽  
Munir R Tanas ◽  
Varun Monga ◽  
Rebecca D Dodd ◽  
...  
Keyword(s):  
Recent Work ◽  
Crucial Role ◽  
Normal Cell ◽  
Cell Function ◽  
Cyclin Dependent Kinase ◽  
Cellular Processes ◽  
Pathway Activation ◽  
Tumor Types ◽  
Sarcoma Treatment ◽  
Insight Into

Sarcomas represent one of the most challenging tumor types to treat due to their diverse nature and our incomplete understanding of their underlying biology. Recent work suggests cyclin-dependent kinase (CDK) pathway activation is a powerful driver of sarcomagenesis. CDK proteins participate in numerous cellular processes required for normal cell function, but their dysregulation is a hallmark of many pathologies including cancer. The contributions and significance of aberrant CDK activity to sarcoma development, however, is only partly understood. Here, we describe what is known about CDK-related alterations in the most common subtypes of sarcoma and highlight areas that warrant further investigation. As disruptions in CDK pathways appear in most, if not all, subtypes of sarcoma, we discuss the history and value of pharmacologically targeting CDKs to combat these tumors. The goals of this review are to (1) assess the prevalence and importance of CDK pathway alterations in sarcomas, (2) highlight the gap in knowledge for certain CDKs in these tumors, and (3) provide insight into studies focused on CDK inhibition for sarcoma treatment. Overall, growing evidence demonstrates a crucial role for activated CDKs in sarcoma development and as important targets for sarcoma therapy.

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