Optimization algorithms and methods
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem. The input to the problem is a multiset of n integers and a positive integer m representing the number of subsets. The goal is to construct, from the input integers, some m subsets. The problem has several variants: * Max-sum MSSP: for each subset j in 1,...,m, there is a capacity Cj. The goal is to make the sum of all subsets as large as possible, such that the sum in each subset j is at most Cj. * Max-min MSSP (also called bottleneck MSSP or BMSSP): again each subset has a capacity, but now the goal is to make the smallest subset sum as large as possible. * Fair SSP: the subsets have no fixed capacities, but each subset belongs to a different person. The utility of each person is the sum of items in his/her subsets. The goal is to construct subsets that satisfy a given criterion of fairness, such as max-min item allocation. (Wikipedia).
Ever wondered what a partial sum is? The simple answer is that a partial sum is actually just the sum of part of a sequence. You can find a partial sum for both finite sequences and infinite sequences. When we talk about the sum of a finite sequence in general, we’re talking about the sum
From playlist Popular Questions
How to multiply two mixed numbers by each other with unlike denominators
👉 Learn how to multiply mixed numbers. To multiply mixed numbers, we first convert the mixed numbers to improper fractions and then multiply the resulting mixed numbers by multiplying the numerator by the numerator and the denominator by the denominator. You can then convert back the resul
From playlist How to Multiply and Divide Fractions
series of n/2^n as a double summation
We will evaluate the infinite series of n/2^n by using the double summation technique. Thanks to Johannes for the solution. Summation by parts approach by Michael Penn: https://youtu.be/mNIsJ0MgdmU Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo 💪 Support this channe
From playlist Sum, math for fun
Determine the Product of a Whole Number and Mixed Number
This video explains how to determine the product of a whole number and mixed number. The product is also modeled. http://mathispower4u.com
From playlist Multiplying and Dividing Mixed Numbers
Determine Multiples of a Given Number
This video explains how to determine the first 4 multiples of a given number. http://mathispower4u.com
From playlist Factors, Prime Factors, and Least Common Factors
Math subsets are an important concept to understand. So what is the subset definition in math? What is a subset? We go over that part of set theory in this video as well as some details on the empty set and its subset properties. Enjoy! I hope you find this video helpful, and be sure to a
From playlist Set Theory
Sum of an Arithmetic Sequence and a Closed Formula for a Sequence of Partial Sums (Reverse and Add)
This video explains how to determine sum of an arithmetic sequence and a closed formula for a sequence of partial sums. A partial sums formula is not used. mathispower4u.com
From playlist Sequences (Discrete Math)
In this video, we introduce the formula for a partial sum of a geometric series
From playlist Sequences and Series
Ex: Find the Product of Three Fractions
This video provides two examples of how to find the product of three fractions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Multiplying and Dividing Fractions
Sophie Stevens: An update on the sum-product problem in R
Discussing recent work joint with M. Rudnev [2], I will discuss the modern approach to the sum-product problem in the reals. Our approach builds upon and simplifies the arguments of Shkredov and Konyagin [1], and in doing so yields a new best result towards the problem. We prove that $max
From playlist Virtual Conference
Subspaces of a vector space. Sums and direct sums.
From playlist Linear Algebra Done Right
Darij Grinberg - The one-sided cycle shuffles in the symmetric group algebra
We study a new family of elements in the group ring of a symmetric group – or, equivalently, a class of ways to shuffle a deck of cards. Fix a positive integer n. Consider the symmetric group S_n. For each 1 ≤ ℓ ≤ n, we define an element t_ℓ := cyc_ℓ + cyc{ℓ,ℓ+1} + cyc_{ℓ,ℓ+1,ℓ+2} + · · ·
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
Proofs involving sets -- Proof Writing 12
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.
From playlist Proof Writing
Nexus Trimester - Mokshay Madiman (University of Delaware)
The Stam region, or the differential entropy region for sums of independent random vectors Mokshay Madiman (University of Delaware) February 25, 2016 Abstract: Define the Stam region as the subset of the positive orthant in [Math Processing Error] that arises from considering entropy powe
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
Part III: Linear Algebra, Lec 1: Vector Spaces
Part III: Linear Algebra, Lecture 1: Vector Spaces Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables
Kim Manuel Klein: On the Fine-Grained Complexity of the Unbounded SubsetSum and Frobenius Problem
Consider positive integral solutions x e Z^(n+1) to the equation a0 * x0 + ... + an * xn = t. In the so called unbounded subset sum problem, the objective is to decide whether such a solution exists, whereas in the Frobenius problem, the objective is to compute the largest t such that ther
From playlist Workshop: Parametrized complexity and discrete optimization
God's Binomial Identity. #SoME2
My submission for SoME2. Please support my research https://paypal.me/feralmathematician?locale.x=en_US
From playlist Summer of Math Exposition 2 videos
Hard Lefschetz Theorem and Hodge-Riemann Relations for Combinatorial Geometries - June Huh
June Huh Princeton University; Veblen Fellow, School of Mathematics November 9, 2015 https://www.math.ias.edu/seminars/abstract?event=47563 A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conj
From playlist Members Seminar
How to multiply two mixed numbers
👉 Learn how to multiply mixed numbers. To multiply mixed numbers, we first convert the mixed numbers to improper fractions and then multiply the resulting mixed numbers by multiplying the numerator by the numerator and the denominator by the denominator. You can then convert back the resul
From playlist How to Multiply and Divide Fractions