scholarly journals Unimodality via Alternating Gamma Vectors

10.37236/5950 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Charles Brittenham ◽  
Andrew T. Carroll ◽  
T. Kyle Petersen ◽  
Connor Thomas
Keyword(s):  
Binomial Coefficient ◽  
The Other ◽  
Combinatorial Proof ◽  
Sufficient Condition ◽  
Proof Of Concept ◽  
Positive Formula

For a polynomial with palindromic coefficients, unimodality is equivalent to having a nonnegative $g$-vector. A sufficient condition for unimodality is having a nonnegative $\gamma$-vector, though one can have negative entries in the $\gamma$-vector and still have a nonnegative $g$-vector.In this paper we provide combinatorial models for three families of $\gamma$-vectors that alternate in sign. In each case, the $\gamma$-vectors come from unimodal polynomials with straightforward combinatorial descriptions, but for which there is no straightforward combinatorial proof of unimodality. By using the transformation from $\gamma$-vector to $g$-vector, we express the entries of the $g$-vector combinatorially, but as an alternating sum. In the case of the $q$-analogue of $n!$, we use a sign-reversing involution to interpret the alternating sum, resulting in a manifestly positive formula for the $g$-vector. In other words, we give a combinatorial proof of unimodality. We consider this a "proof of concept" result that we hope can inspire a similar result for the other two cases, $\prod_{j=1}^n (1+q^j)$ and the $q$-binomial coefficient ${n\brack k}$.

scholarly journals Chromatin Manipulation and Editing: Challenges, New Technologies and Their Use in Plants

2021 ◽  
Vol 22 (2) ◽  
pp. 512
Author(s):  
Kateryna Fal ◽  
Denisa Tomkova ◽  
Gilles Vachon ◽  
Marie-Edith Chabouté ◽  
Alexandre Berr ◽  
...  
Keyword(s):  
Cell Fate ◽  
Dna Sequence ◽  
Zinc Finger ◽  
Chromatin Structure ◽  
New Technologies ◽  
Dna Interaction ◽  
The Other ◽  
Proof Of Concept ◽  
Epigenetic Marks ◽  
Molecular Events

An ongoing challenge in functional epigenomics is to develop tools for precise manipulation of epigenetic marks. These tools would allow moving from correlation-based to causal-based findings, a necessary step to reach conclusions on mechanistic principles. In this review, we describe and discuss the advantages and limits of tools and technologies developed to impact epigenetic marks, and which could be employed to study their direct effect on nuclear and chromatin structure, on transcription, and their further genuine role in plant cell fate and development. On one hand, epigenome-wide approaches include drug inhibitors for chromatin modifiers or readers, nanobodies against histone marks or lines expressing modified histones or mutant chromatin effectors. On the other hand, locus-specific approaches consist in targeting precise regions on the chromatin, with engineered proteins able to modify epigenetic marks. Early systems use effectors in fusion with protein domains that recognize a specific DNA sequence (Zinc Finger or TALEs), while the more recent dCas9 approach operates through RNA-DNA interaction, thereby providing more flexibility and modularity for tool designs. Current developments of “second generation”, chimeric dCas9 systems, aiming at better targeting efficiency and modifier capacity have recently been tested in plants and provided promising results. Finally, recent proof-of-concept studies forecast even finer tools, such as inducible/switchable systems, that will allow temporal analyses of the molecular events that follow a change in a specific chromatin mark.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals Equipartitioning and balancing points of polygons

Pythagoras ◽  
2010 ◽  
Vol 0 (71) ◽  
Author(s):  
Shunmugam Pillay ◽  
Poobhalan Pillay
Keyword(s):  
General Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

scholarly journals Transferrin-Conjugated SNALPs Encapsulating 2′-O-Methylated miR-34a for the Treatment of Multiple Myeloma

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Immacolata Scognamiglio ◽  
Maria Teresa Di Martino ◽  
Virginia Campani ◽  
Antonella Virgilio ◽  
Aldo Galeone ◽  
...  
Keyword(s):  
Multiple Myeloma ◽  
Zeta Potential ◽  
Lipid Vesicles ◽  
Significant Inhibition ◽  
The Other ◽  
Transferrin Receptors ◽  
Proof Of Concept ◽  
Wild Type ◽  
Chemical Conjugation ◽  
Mean Size

Stable nucleic acid lipid vesicles (SNALPs) encapsulating miR-34a to treat multiple myeloma (MM) were developed. Wild type or completely 2′-O-methylated (OMet) MiR-34a was used in this study. Moreover, SNALPs were conjugated with transferrin (Tf) in order to target MM cells overexpressing transferrin receptors (TfRs). The type of miR-34a chemical backbone did not significantly affect the characteristics of SNALPs in terms of mean size, polydispersity index, and zeta potential, while the encapsulation of an OMet miR-34a resulted in a significant increase of miRNA encapsulation into the SNALPs. On the other hand, the chemical conjugation of SNALPs with Tf resulted in a significant decrease of the zeta potential, while size characteristics and miR-34a encapsulation into SNALPs were not significantly affected. In an experimental model of MM, all the animals treated with SNALPs encapsulating miR-34a showed a significant inhibition of the tumor growth. However, the use of SNALPs conjugated with Tf and encapsulating OMet miR-34a resulted in the highest increase of mice survival. These results may represent the proof of concept for the use of SNALPs encapsulating miR-34a for the treatment of MM.

scholarly journals Two examples related to conical energies

2022 ◽  
Vol 47 (1) ◽  
pp. 261-281
Author(s):  
Damian Dąbrowski
Keyword(s):  
Singular Integral ◽  
Recent Article ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
The Other ◽  
Independent Interest ◽  
Sufficient Condition ◽  
Lipschitz Graphs ◽  
Big Pieces

In a recent article (2021) we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

scholarly journals Combinatorial Proof of a Curious $q$-Binomial Coefficient Identity

10.37236/462 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Victor J. W. Guo ◽  
Jiang Zeng
Keyword(s):  
Binomial Coefficient ◽  
Combinatorial Proof ◽  
Binomial Coefficient Identity

Using the Algorithm Z developed by Zeilberger, we give a combinatorial proof of the following $q$-binomial coefficient identity $$ \sum_{k=0}^m(-1)^{m-k}{m\brack k}{n+k\brack a}(-xq^a;q)_{n+k-a}q^{{k+1\choose 2}-mk+{a\choose 2}} $$ $$=\sum_{k=0}^n{n\brack k}{m+k\brack a}x^{m+k-a}q^{mn+{k\choose 2}}, $$ which was obtained by Hou and Zeng [European J. Combin. 28 (2007), 214–227].

scholarly journals A Welcome to the New Journal, Journal of Advanced Therapies and Medical Innovation Science (j.ATAMIS).

2016 ◽  
Vol 1 ◽  
Author(s):  
Andrew Coats ◽  
Louise Shewan
Keyword(s):  
Venture Capital ◽  
Medical Devices ◽  
Medical Science ◽  
The Other ◽  
Proof Of Concept ◽  
Medical Innovation ◽  
Start Up ◽  
Advanced Therapies ◽  
Publishing Journal

<p>A new journal has been launched by Barcaray Publishing: Journal of Advanced Therapies and Medical Innovation Sciences (J.ATAMIS, www.j-atamis.org).  This journal fills a crucial gap in the literature – and in the cycle of advances in medical science, therapeutics and devices - covering the pipeline from idea through proof of concept studies and start-up funding to regulatory approval.  It will be multi-disciplinary and unusually we will have significant input from funders - both angel and venture capital-, start-up CEO’s, and regulators as well as medical scientists and triallists.  We have quite frankly a stellar editorial board, with leading lights of biotechnology, medical devices, new and established pharma as well as the “other side”, CEO’s and investors.  </p>

Interface acoustic waves in piezoelectric bi-crystalline structures of specific types

2005 ◽  
Vol 461 (2056) ◽  
pp. 895-911 ◽  
Author(s):  
A. N Darinskii ◽  
M Weihnacht
Keyword(s):  
Acoustic Waves ◽  
The Other ◽  
Imaginary Component ◽  
Sufficient Condition ◽  
Bulk Wave ◽  
Piezoelectric Crystal ◽  
Piezoelectric Media ◽  
Crystalline Structures ◽  
Material Constants ◽  
Bulk Waves

The paper discusses the properties of the acoustic waves guided by an interface inside piezoelectric media. The interfaces of two types have been considered: (i) an infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry; (ii) rigidly bonded crystals whose piezoelectric coefficients differ by sign while the other material constants are identical. Several general theorems have been proved regarding the existence of interface acoustic waves (IAWs) propagating more slowly than bulk waves. In particular, a sufficient condition for the existence of such ‘slow’ IAWs has been derived. The propagation of leaky IAWs has been studied. Special attention has been paid to the analysis of the situation when the imaginary component of the leaky IAW velocity vanishes, resulting in the appearance of non-attenuating IAWs travelling faster than the slow transverse bulk wave. The computations performed for LiNbO 3 and LiTaO 3 illustrate general conclusions.

Trustworthy Government and Legitimating Beliefs

2019 ◽  
pp. 362-384
Author(s):  
Margaret Levi
Keyword(s):  
Decision Making ◽  
State Building ◽  
The Other ◽  
Sufficient Condition ◽  
Goods And Services ◽  
Moral Economies ◽  
The Government ◽  
The Relationship ◽  
Advanced Democracies

A trustworthy government is one that keeps its promises (or has exceptionally good reasons why it fails to), is relatively fair in its decision-making and enforcement processes, and delivers goods and services. A legitimate government is one that appeals to widely accepted justifications for its selection, maintenance, and policies. Investigations across history and countries reveal that the more trustworthy the government, the more likely it is to evoke observation of its laws and acquiescence to policies. Less clear is the link between perceptions that government is trustworthy and beliefs that it is legitimate, at least in countries claiming or trying to be democratic. Being trustworthy in practices and outcomes may contribute to perceptions of government legitimacy. However, trustworthiness is, at best, a necessary but not sufficient condition for legitimating beliefs. This chapter explores the relationship between the trustworthiness of government and its legitimacy by considering cases from both advanced democracies and state-building efforts. It argues that current democracies may need to refashion their moral economies—the extra-market reciprocal rights and obligations that link populations, governments, corporations, and all the other various organizations that make up the society—if they are to reestablish strong grounds for legitimacy.

scholarly journals How Much Information Does a Robot Need? Exploring the Benefits of Increased Sensory Range in a Simulated Crowd Navigation Task

Information ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 112
Author(s):  
Marit Hagens ◽  
Serge Thill
Keyword(s):  
Task Performance ◽  
Human Robot Interaction ◽  
The Other ◽  
Proof Of Concept ◽  
Robot Interaction ◽  
Navigation Task ◽  
Navigation Strategy ◽  
Hardware Designs ◽  
Navigation Strategies ◽  
And Task

Perfect information about an environment allows a robot to plan its actions optimally, but often requires significant investments into sensors and possibly infrastructure. In applications relevant to human–robot interaction, the environment is by definition dynamic and events close to the robot may be more relevant than distal ones. This suggests a non-trivial relationship between sensory sophistication on one hand, and task performance on the other. In this paper, we investigate this relationship in a simulated crowd navigation task. We use three different environments with unique characteristics that a crowd navigating robot might encounter and explore how the robot’s sensor range correlates with performance in the navigation task. We find diminishing returns of increased range in our particular case, suggesting that task performance and sensory sophistication might follow non-trivial relationships and that increased sophistication on the sensor side does not necessarily equal a corresponding increase in performance. Although this result is a simple proof of concept, it illustrates the benefit of exploring the consequences of different hardware designs—rather than merely algorithmic choices—in simulation first. We also find surprisingly good performance in the navigation task, including a low number of collisions with simulated human agents, using a relatively simple A*/NavMesh-based navigation strategy, which suggests that navigation strategies for robots in crowds need not always be sophisticated.

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