Related Experiment Video
Updated: Jul 7, 2025

Long-term Video Tracking of Cohoused Aquatic Animals: A Case Study of the Daily Locomotor Activity of the Norway Lobster Nephrops norvegicus
Published on: April 8, 2019
Log concavity for unimodal sequences
Walter Bridges1, Kathrin Bringmann1
1Universität zu Köln: Universitat zu Koln, Cologne, Germany.
Abstract:
In this paper, we prove that the number of unimodal sequences of size n is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact formula due to recent work of the second author and Nazaroglu on false theta functions. Log-concavity and higher Turán inequalities have been well-studied for (restricted) partitions and coefficients of weakly holomorphic modular forms, and analytic proofs generally require precise asymptotic series with error term. In this paper, we proceed from the exact formula for unimodal sequences to carry out this calculation. We expect our method applies to other exact formulas for coefficients of mixed mock/false modular objects.
More Related Videos
08:27Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
Published on: January 5, 2024
15:07VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma
Published on: December 28, 2015
Related Concept Videos
Per-Unit Sequence Models
Zero-sequence currents, which are identical in magnitude and phase, generate a neutral current, resulting in voltage drops across the neutral impedance and the low-voltage winding. If the...
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
Cumulative Frequency Distribution
Probability Histograms
Curvilinear Motion: Rectangular Components
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...