Richard Hoshino Quest University Canada

Game Of Fifteen There are nine integers on the whiteboard: You and I take turns selecting one of these numbers, and then crossing it off the board. The winner is the first person to select three numbers adding up to 15. Can you beat me?

Playing Tic-Tac-Toe! The Game of Fifteen is identical (isomorphic) to Tic-Tac-Toe!

Eureka Moment I am really good at recognizing isomorphisms, i.e., situations when hard real-life societal problems can be converted into simpler equivalent math problems. This is because of my training in Discrete Mathematics, especially in graph theory and combinatorics.

PART ONE HIGH SCHOOL OUTREACH

CMS National Math Camp 6

Nova Scotia Math League 7

Nova Scotia Math Circles 8

Writing a Novel

Papers from my Ph.D. Thesis

PART TWO MATH IN GOVERNMENT

Canada Border Services Agency 12

Marine Container Shipping 13

Improving Risk-Assessment 14

Reducing Wait Times 15

Iris Biometrics Source:

Hamming Distance Comparison Say a passenger has the following 20-digit iris code: Compare it to each of the images/codes in the gallery: Image HD Alice Bob Carol

Hamming Distance Comparison Say a passenger has the following 20-digit iris code: Compare it to each of the images/codes in the gallery: Image HD Alice Bob Carol

Hamming Distance Comparison Say a passenger has the following 20-digit iris code: Compare it to each of the images/codes in the gallery: Image HD Alice0.55 Bob Carol

Hamming Distance Comparison Say a passenger has the following 20-digit iris code: Compare it to each of the images/codes in the gallery: Image HD Alice0.55 Bob0.50 Carol

Hamming Distance Comparison Say a passenger has the following iris code: Compare it to each of the images/codes in the gallery: HD Alice0.55 Bob0.50 Carol0.10 Passenger is Carol

Genuine and Impostor Matches Genuine Distribution u* = 0.09, m* = 49

Calibrated Confidence Scoring

PART THREE JAPANESE BASEBALL LEAGUE

Our Life in Chiba, Japan Our Apartment Kanda University Chiba Marine StadiumTrain Station

Chiba Lotte Marines

Victory Parade in Chiba

Life in Toronto…

Inspiration

Unexpected Inspiration

Key Insight R2 TFOSH COSHF OSFTC HTCFS SCHOT FHTCO R3 TFOSH CHSFO STFOC FSCHT OCHTS HOTCF R1 SHTFO HFCOS TCOSF FSHTC OTSCH COFHT R4 OSHTF SFOCH FOCST CHTFS HTSOC TCFHO

Chiba Marines Schedule (2010) (HOME sets are marked in red.)

Nippon Pro Baseball Schedules Five Conditions: At-Most-Three No-Repeat Home-Away Each-Round Diff-Two |H−R| ≤ 2

Traveling Tournament Problem Given an n × n distance matrix, determine the double round-robin tournament schedule that satisfies At-Most-Three, No-Repeat, and Home-Away. minimizes the total distance traveled by the n teams.

An Example A-B-C-B-A – C-D-E-D-E is a valid team schedule under the Traveling Tournament Problem (TTP) but not for the Japanese Pro Baseball (violates Each-Round and Diff-Two).

History of the TTP TTP-solving algorithms are a complex hybrid of integer programming and constraint programming. The TTP is NP-complete. Best solved instance is 10 teams.

Multi-Round Balanced TTP Given an n × n distance matrix, find the distance-optimal tournament schedule that lasts 2k rounds (k blocks) and satisfies all five conditions: At-Most-Three, No-Repeat, Home-Away, Each-Round, Diff-Two.

Graph-Theoretic Reformulation The length of the tournament is 2k rounds. We create a graph on 2km+2 vertices.

Explanation of the variable m 12 D1 E1 F1 A0 B0 C0 Team A B C D E F For n = 6, m = 120 × 20 = In general, There are ways to select the home teams of any column. So there are ways to select the three matches of any column.

Graph-Theoretic Reformulation

Each team starts and ends the season at home (v start, v end )

Graph-Theoretic Reformulation Each vertex x t,u with 1 ≤ u ≤ m, represents the first two columns of the t th block (matches then home teams)

Graph-Theoretic Reformulation Each vertex y t,u with 1 ≤ u ≤ m, represents the last two columns of the t th block (home teams then matches)

The Edges x t,u → y t,v

Construction of Edge x t,u → y t,v 12 B0 A0 F0 E1 D1 C1 Team A B C D E F 910 1F 0E 1D 1C 0B 0A x 1,u y 1,v x t,u → y t,v is an edge iff there exists a (feasible) block satisfying the five conditions. The weight of edge x t,u → y t,v is the minimum possible total distance traveled by the n teams within that block ?????? ?????? ?????? ?????? ?????? ??????

The Edges y t,v → x t+1,u

Construction of Edge y t,v → x t+1,u Team A B C D E F 910 1F 0E 1D 1C 0B 0A 1112 B0 A0 F0 E1 D1 C1 y 1,v x 2,u y t,v → x t+1,u is an edge iff the n × 4 concatenation matrix does not violate the at-most-three or no-repeat conditions. The weight of edge y t,v → x t+1,u is the distance traveled by the n teams moving from set 2t(n-1) to 2t(n-1)+1.

Dijkstra’s Algorithm The directed graph has 2mk+2 vertices and at most 2m+(2k-1)m 2 edges. Each edge has a weight. Now apply Dijkstra’s Algorithm to find the shortest path v start → x 1,u1 → y 1,v1 → … → x k,uk → y k,vk → v end which produces the optimal solution of the mb-TTP.

Optimal NPB Schedule In the NPB, each team plays 120 intra-league games (40 sets of 3 games), with eight sets (24 games) against each of the other 5 teams. Thus, there are 8 rounds. TeamR1R2R3R4R5R6R7R8 Chiba SHTFOTFOSH OSHTFHOFSTFSTHOTSHOFHOFTS Tohoku HFCOSCOSHFCHSFOSFOCHSHOFCOFCSHCHOFSOFSCH Hokkaido TCOSFOSFTCSTFOCFOCSTCTSOFSOFCTFTCSOCSOFT Orix FSHTCHTCFSFSCHTCHTFSFCTHSTHSFCSFTCHTCHSF Fukuoka OTSCHSCHOTOCHTSHTSOCOSCTHCTHOSHOSTCSTCHO Saitama COFHTFHTCOHOTCFTCFHOTFHCOHCOTFOCFHTFHTOC

Results for NPB Pacific League For the 6-team NPB Central League, we achieve a 26.8% reduction in total travel distance 14.6% reduction in total trips taken. Team NameDistance (2010) Distance (New) Reduction in Travel Trips (2010) Trips (New) Reduction in Trips Chiba23,26616, % % Tohoku23,71017, % % Hokkaido28,59920, % % Orix24,12818, % % Fukuoka33,35221, % % Saitama20,88519,4986.6% % TOTAL153,940114, % %

Nippon Pro Baseball League

NPB Requirements 1) Weekday and Weekend balancing 20 weekday sets (half home, half away) 20 weekend sets (half home, half away) 2) If possible, enforce at-most-two (no 3-set home stands, 3-set road trips)

Results with New Requirements ScheduleDistanceTrips Central League (2012)86, mb-TTP (Five Conditions)57, All Seven Conditions66, Conditions + Constraints76, Final Central League Schedule (2013) 80,006194

Inspiring Change with Research

PART FOUR QUEST UNIVERSITY CANADA

Inspiring Change at Quest 1) A new Roommate Matching algorithm More efficient, increased compatibility 2) A new Course Registration System More equitable, increased effectiveness 58

Conclusion We make a living by what we get. We make a life by what we give. Winston Churchill 59