text:
The Top 15 Best Talent Management Books
Sometimes, in order to advance technologically, it's helpful to look at an old-school approach. Talent management systems are essential for your organization, but you should first ensure that it's right for you and your team. While there are many free resources available online, (such as Solutions Review's best practices articles, solutions directories, and buyer's guides), doing things the old-fashioned way can be beneficial. Solutions Review has taken the liberty of doing the research for you, having reviewed a multitude of books. We've carefully selected the best talent management books based on relevance, popularity, review ratings, publish date, and ability to add business value. Here they are in no particular order.
Global Talent Management (Global HRM)
By Hugh Scullion, Paula M. Caligiuri, and David G. Collings
"Drawing on contributions from the leading global contributors to talent management research, the book is structured around three key sections. Section one provides a contextual overview of talent management. The second section explores in depth some of the core areas of GTM practice which includes the meaning of talent in the global context, internal talent identification, developing leadership talent, employee turnover, employer branding and the role of the corporate HR function in GTM. The final section considers three key contemporary issues in GTM, namely, data analytics in GTM, managing virtual talent and managing globally diverse talent."
Managing to Make a Difference: How to Engage, Retain, and Develop Talent for Maximum Performance
By Larry Sternberg and Kim Turnage
"Most organizations direct the majority of their development resources to the C-suite, but still expect their mid-level managers to attract, engage, retain, and develop talent; but successfully juggling everyday duties while maintaining team performance and leading around roadblocks leaves little room for management planning. Managing to Make a Difference offers the solution in the form of tools, techniques, and practical strategy for a high performing team."
The Alliance: Managing Talent in the Networked Age
By Reid Hoffman, Ben Casnocha, and Chris Yeh
"Coauthored by the founder of LinkedIn, this bold but practical guide for managers and executives will give you the tools you need to recruit, manage, and retain the kind of employees who will make your company thrive in today's world of constant innovation and fast-paced change."
The Problem Isn't Their Paycheck: How to Attract Top Talent and Build a Thriving Company Culture
By Grant Botma
"If you're an entrepreneur who's spending too much time working in your business, this book will allow you to finally start working on your business. Grant Botma shows you how to transform your hiring and management practices to build a thriving team of top performers that will handle the day-to-day tasks so you can have freedom and deliver value to the business in ways nobody else can."
The Talent Manifesto: How Disrupting People Strategies Maximizes Business Results
By RJ Heckman
"The Talent Manifesto reveals proven talent strategies and innovative recruiting and retainment methods gleaned from nearly three decades of consulting with the world's leading organizations. Heckman identifies the most common pitfalls in HR today and delivers an actionable program for avoiding them. He shows how to generate reliable data and use it to make the best decisions. He reveals all the game-changing HR strategies at your disposal and how to use them to drive superior business performance."
Talent Generation: How Visionary Organizations are Redefining Work and Achieving Greater Success
By Sarah Sladek
"Drawing from documented workforce and talent-development research, as well as her own ongoing study of generational impacts, Sarah Sladek cites numerous examples of organizations that have been capable of engaging employees in this era of disruption what they did, why it worked, and how it's made a difference to the organizations outlook and bottom line."
Human Resource Management: People, Data, and Analytics
By Tayla Bauer, Berrin Erdogan, David E. Caughlin, and Donald M. Truxillo
"Human Resource Management: People, Data, and Analytics by Talya Bauer, Berrin Erdogan, David Caughlin, and Donald Truxillo introduces students to the fundamentals of talent management with integrated coverage of data analytics and how they can be used to inform and support decisions about people in an organization. Features tied to SHRM competencies and data exercises give readers hands-on opportunities to practice the analytical and decision-making skills they need to excel in today's job market. Engaging examples illustrate key HRM concepts and theories, which brings many traditional HRM topics concepts to life. Whether your students are future managers or future HR professionals, they will learn best practices for managing talent across the lifecycle in the changing workplace."
The Talent Management Handbook, Third Edition: Making Culture a Competitive Advantage by Acquiring, Identifying, Developing, and Promoting the Best People
By Lance Berger and Dorothy Berger
"The Talent Management Handbook is the established go-to guide for HR professionals, managers, and leaders looking for the best ways to use talent management programs to develop a culture of excellence. This third edition features new and updated chapters based on fresh approaches and material for identifying, recruiting, positioning, and developing highly qualified, motivated people to meet current and future business requirements. Filled with expert advice, the book offers a roadmap for developing a comprehensive approach to talent management that will guide professionals in the coming years."
One Page Talent Management with a New Introduction: Eliminating Complexity, Adding Value
By Marc Effron and Miriam Ort
"Effron and Ort introduce a simple, powerful, scientifically proven approach to increase your ability to develop better leaders faster: One Page Talent Management (OPTM). Using the straightforward, easy-to-follow process described in this book, you will eliminate frustrating complexity, focus only on those components that add real value, and build transparency and accountability into every practice."
Talent Magnet: How to Attract and Keep the Best People (The High Performance Series)
By Mark Miller
"More than vision, strategy, creativity, marketing, finance, or even technology, it is ultimately people that determine organizational success. That's why virtually every organization wants more top talent. But do you know what they're looking for? It might not be what you think! Talent Magnet will show you how to attract and keep great people."
Bet on Talent: How to Create a Remarkable Culture That Wins the Hearts of Customers
By Dee Ann Turner
"When it comes to running a business, the most important decisions a leader makes are not about products or locations–they're about people. For the past 33 years, Dee Ann Turner has been recruiting, training, and retaining some of the best employees in the restaurant business. Now she's ready to share her secrets on how to build, sustain, and grow an organizational culture that attracts world-class talent and consistently delights customers, no matter what your industry."
Demystifying Talent Management: Unleash People's Potential to Deliver Superior Results
By Kimberly Janson
"Demystifying Talent Management offers practical advice for all managers, HR professionals, senior leaders, and other employees on how to work together to build a talented and motivated workforce. The book addresses performance, development, coaching, feedback, compensation, and other elements of people management. Using simple, straightforward language, Kim Janson tells you how you can avoid confusion and conflicts when engaging in talent management."
Inclusive Talent Management: How Business Can Thrive in an Age of Diversity
By Stephen Frost and Danny Kalman
"Featuring case studies from internationally recognised brands such as Goldman Sachs, Unilever, KPMG, Hitachi, Oxfam and the NHS, Inclusive Talent Management shows that to achieve business objectives and gain the competitive advantage, it is imperative that organizations take an inclusive approach to talent management. It puts forward a compelling and innovative case, raising questions not only for the HR community but also to those in senior management positions, providing the practical steps, global examples and models for incorporating diversity and inclusion activities into talent management strategy."
Aha Moments in Talent Management: A Business Fable with Practical Exercises
By Mark Allen
"Most executives would say that people are their most valuable asset; but even with the best intentions of putting employees first, companies can be held back by outdated policies. This business fable highlights 13 talent management principles, illustrating them in action at a fictional company with a charismatic and passionate Chief People Officer."
The Essential HR Handbook, 10th Anniversary Edition: A Quick and Handy Resource for Any Manager or HR Professional
By Sharon Armstrong and Barbara Mitchell
"Whether you're a small business owner, a manager in a business without an HR department, or even a seasoned HR professional, The Essential HR Handbook will help you handle any personnel problem–from onboarding to outplacement–quickly and easily. This fully updated 10th anniversary edition is packed with information, tools, checklists, sample forms, and timely tips to guide you through the maze of personnel issues in today's complex business environment."
Tess Hanna
Tess Hanna is an editor and writer at Solutions Review covering Backup and Disaster Recovery. She has a degree in English and Textual Studies from Syracuse University. You can contact her at thanna@solutionsreview.com
LinkedInTwitterFacebookTaggedBooksHCMHRHR TechnologyHuman ResourcesTalent ManagementTalent Management Books
PreviousPrevious post:The Features You Need in Your Talent Management Solution
Ditch the Annual Performance Reviews. This is How Progressive Companies Do It
Admit it. You can't stand preparing and delivering employee reviews. This process offers many benefits and takes the pain out of the process for everyone.
By Marla Tabaka@MarlaTabaka Source Inc
Have you ever met a manager or an employee who looks forward to the annual review process? It's not likely. This SHRM study found that as many as 72% of companies still conduct yearly reviews even though 87% of both managers and employees find them ineffective. And, an Adobe study found that 41% of employees would go so far as to change jobs to avoid this grueling process.
Why annual reviews are ineffective.
Have you ever been asked by a medical professional to rate your pain on a scale of zero to 10? It's nearly impossible to label it with an absolute number. "Oh, it's about a four-and-a-half," you might say. Or, "Somewhere between five and eight."
Standard annual reviews ask managers to assign a numeric value to their employees' performance, which is impossible. Performance and value are subjective, depending on the circumstances at any given moment. Employees are humans, not numbers; no one wants to be graded and labeled.
Companies like Adobe, General Electric, and Cigna have ousted the annual review process in favor of frequent, individualized feedback. They have indicated a greater sense of inclusiveness and camaraderie, which are core to a thriving company culture.
This is how annual reviews usually play out.
If you perform annual reviews for your employees, you probably approach it like most of my clients have done in the past. You begin pressuring yourself to get the review done about two weeks before the due date. You dread the process and wonder where you're going to find the time. As you're driving to work, you might think about the employee and try to remember their mistakes and achievements over the past 12 months. Lastly, you stay up all night to work on the review and deliver it to a very uncomfortable employee the next day. Frequently, months past the anniversary date.
Is a review beneficial enough to merit all of this agony and stress?
Let's look at the benefits.
One-to-one time with your employee--everyone wants the boss's attention.An opportunity to let them know how much value they bring to the company and how much you appreciate them.Feedback to facilitate growth.Goal setting for the next year.The reward of giving and receiving a raise or bonus.An opportunity for the employee to voice their desires for the future, and other feedback and questions. A means to have a record about the employee's performance on file.
In reviewing this list of benefits, here's the first thing I notice: Each one of them should be a part of an ongoing process all year round, except for raises, of course. A Gallup study revealed that employees whose managers regularly communicate with them are nearly three times more engaged than those with managers who don't communicate regularly. The benefits related to frequent feedback, goal setting, and growth opportunities far outweigh the value of an annual review. The entrepreneurs I've worked with have observed improved morale and increased engagement and performance. In many cases, it's prevented potentially serious issues from cropping up.
There are potential pitfalls even to this more progressive and constructive approach. Here are a few tips on how to make your transition smoothe.
Take notes.
Doing away with annual reviews does not preclude the need for documentation. Keep ongoing notes on your discussions and the action steps that result from them. In the case of an underperforming employee, this is especially important.
Discuss reward and compensation.
Tell employees when and if they can expect a raise. The absence of an annual review could leave employees wondering about their financial future with the company.
Don't slack.
It's great when you stop someone in the hallway to acknowledge an achievement, but a scheduled meeting still needs to take place. I have one client who meets with each of her five employees weekly, some of my clients hold meetings with employees monthly, and some quarterly. Determine your schedule by considering goals for your culture, the stage of growth the company is in, and how employees are performing. Avoid putting off a meeting with an employee for any reason; this sends the message that they don't come first.
These meetings aren't about you; they are about the employee. Your time together is the perfect opportunity to ask them questions about their ideas and vision. Ask them for feedback about your leadership and communication style and let them voice their general concerns should there be any.
Whether you have one or 100 employees, these changes may benefit you greatly. Begin developing your new process slowly if it feels more comfortable to you. Over the next year, meet with employees individually to minimize the work and stress of your annual meeting. Measure your success by observing increased engagement, productivity, contribution, and happiness.
PUBLISHED ON: NOV 30, 2019The opinions expressed here by Inc.com columnists are their own, not those of Inc.com.
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Xavier has a long experience in b2b marketing, lead generation and business development, as well as Salesforce solutions. Through this booklet, he will show you how marketing and sales can create joint campaigns to stimulate your sales funnel.
At Incloud, we believe that cloud technologies can improve the efficiency of any business organizations. With Salesforce marketing automation solutions, we help you reach out the right prospect at the right time. Based in Montreal, Incloud is able to configure your instance, customize your templates and train your team with Marketing Automation.


If you have a Tennessee Taxpayer Access Point (TNTAP) account with the Tennessee Department of Revenue, you can update your address by logging into your TNTAP account and updating your account information.
Or, you can contact the Taxpayer Services Division at (800) 342-1003 (in-state) or (615) 253-0600.
How do I change my address using TNTAP?


Despite the initial costs, renovating a store can offer big returns. Retail sales get a nearly 50 percent boost when a shop gets a new look.
A new study looks at how both first-time visitors and existing customers react when retailers undertake major remodeling of their premises.
Stores are remodeled every seven to 10 years on average. Because shopping is an important part of daily life for many people, the financial return on investment has the potential to be substantial, says Tracey Danaher, professor of marketing at Monash University.
The findings, published in the Journal of Marketing, show sales to new customers increase by 43 to 44 percent after remodeling, and those to existing customers go up by seven to 10 percent.
"We found sales for new customers were significantly higher than those for existing customers after the remodel, and this difference persisted for a year," Danaher says.
Store remodeling should be regarded as a marketing investment, designed to retain and attract new customers, similar to mainstream advertising, Danaher says.
"It is vital that retail firms understand how remodeling the store layout influences customer perceptions and purchase behavior.
"New customers' perceptions of the retail environment—including its atmosphere and layout—were much higher than those of existing customers. They also perceived significantly greater service quality and higher levels of customer satisfaction.
The study also shows the difference between new and existing customers endure for the long run.
"Store remodeling is expensive, so managers must weigh the benefits against the costs," Danaher says.


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Q: Realtime MIDI Events with NAudio and VST.NET I have the following code working great with VST Effects, passing a sinewave in and receiving a result without any glitches. However, I need to pass in a custom created MIDI Event (using either VST.NET or NAudio MIDI Helpers), and am having no luck. Is it because the absolute and deltaframes are zero? I don't know where else to turn, and have been banging my head against the keyboard for a while now.
In monitoring the debug window, I can see that the VST Events are being picked up by the plugin. I also went ahead and created a custom plugin to make sure that I was receiving the Event info, and it is being passed through properly. I just don't get any audio output!
In the code example, all you will have to do to make this work is:
A. place a VSTi dll (which has two Audio Output channels, and accepts VST MIDI Input) in the bin\debug folder when you debug this
B. change the name of the VSTi dll from cobalt.dll to whatever the name is of the VST you are using to test.
It is a Windows Universal XML Page with one button, btnTest
Imports NAudio.Wave
Imports NAudio.Midi
Imports Jacobi.Vst.Core
Imports Jacobi.Vst.Interop.Host

Class MidiTestPage
Private waveOut As WaveOut
Private ctx As VstPluginContext

Private Sub btnTest_Click(sender As Object, e As EventArgs) Handles btnTest.Click
    Dim pluginPath As String = System.AppDomain.CurrentDomain.BaseDirectory & "VSTPlugins\" & "cobalt.dll"
    ctx = InitPlugin(pluginPath, 1)
    Dim midiWaveProvider As New MidiSampleProvider(ctx)
    If waveOut Is Nothing Then
        waveOut = New WaveOut(WaveCallbackInfo.FunctionCallback())
        waveOut.Init(midiWaveProvider)
        waveOut.Volume = 1.0
        waveOut.Play()
    End If
End Sub

Private Sub HostCmdStub_PluginCalled(sender As Object, e As PluginCalledEventArgs)
    Dim hostCmdStub As HostCommandStub = DirectCast(sender, HostCommandStub)
    Try
        ' can be null when called from inside the plugin main entry point.
        If hostCmdStub.PluginContext.PluginInfo IsNot Nothing Then
            Debug.WriteLine("Plugin " & hostCmdStub.PluginContext.PluginInfo.PluginID & " called:" & e.Message)
        Else
            Debug.WriteLine("The loading Plugin called:" & e.Message)
        End If
    Catch ex As Exception
        Debug.WriteLine("The loading Plugin called:" & e.Message)
    End Try

End Sub

Private Function InitPlugin(pluginPath As String, programIndex As Integer) As VstPluginContext
    Dim hostCmdStub As New HostCommandStub()
    AddHandler hostCmdStub.PluginCalled, AddressOf HostCmdStub_PluginCalled
    Dim ctx As VstPluginContext = VstPluginContext.Create(pluginPath, hostCmdStub)
    'plugins.Add(ctx)
    ' add custom data to the context
    ctx.Set(Of String)("PluginPath", pluginPath)
    ctx.Set(Of HostCommandStub)("HostCmdStub", hostCmdStub)
    '' actually open the plugin itself
    ctx.PluginCommandStub.Open()
    ctx.PluginCommandStub.MainsChanged(True)
    ctx.PluginCommandStub.BeginSetProgram()
    ctx.PluginCommandStub.SetProgram(programIndex)
    ctx.PluginCommandStub.EndSetProgram()
    ctx.PluginCommandStub.StartProcess()
    Return ctx
End Function
End Class

Public Class MidiSampleProvider
Implements ISampleProvider
Private pluginContext As VstPluginContext

Public Shadows ReadOnly Property WaveFormat As WaveFormat Implements ISampleProvider.WaveFormat
    Get
        Return WaveFormat.CreateIeeeFloatWaveFormat(44100, 2)
    End Get
End Property
Private BlockSize As Integer = 0
Private inputBuffers As VstAudioBuffer()
Private outputBuffers As VstAudioBuffer()
Dim vEvents As List(Of VstEvent)

Public Sub New(ctx As VstPluginContext)
    pluginContext = ctx
    vEvents = New List(Of VstEvent)
    CreateMidiEvent(pluginContext)
End Sub

Private Sub UpdateBlockSize(blockSize__1 As Integer)
    BlockSize = blockSize__1

    Dim inputCount As Integer = pluginContext.PluginInfo.AudioInputCount
    Dim outputCount As Integer = pluginContext.PluginInfo.AudioOutputCount

    Dim inputMgr = New VstAudioBufferManager(inputCount, blockSize__1)
    Dim outputMgr = New VstAudioBufferManager(outputCount, blockSize__1)

    pluginContext.PluginCommandStub.SetBlockSize(blockSize__1)
    pluginContext.PluginCommandStub.SetSampleRate(WaveFormat.SampleRate)
    pluginContext.PluginCommandStub.SetProcessPrecision(VstProcessPrecision.Process32)

    inputBuffers = inputMgr.ToArray()
    outputBuffers = outputMgr.ToArray()

End Sub

Public Function Read(buffer() As Single, offset As Integer, count As Integer) As Integer Implements ISampleProvider.Read
    Dim samplesRequired As Double = count / 2
    If samplesRequired <> BlockSize Then
        UpdateBlockSize(samplesRequired)
    End If
    Dim samplesRead As Double = 0
    If vEvents.Count > 0 Then
        pluginContext.PluginCommandStub.ProcessEvents(vEvents.ToArray)
        pluginContext.HostCommandStub.ProcessEvents(vEvents.ToArray)
        pluginContext.PluginCommandStub.ProcessReplacing(inputBuffers, outputBuffers)
        'vEvents.Clear()
    End If
    For j As Integer = 0 To BlockSize - 1
        buffer(samplesRead + offset) = outputBuffers(0)(j)
        samplesRead += 2
    Next
    Return samplesRead
End Function

Public Sub CreateMidiEvent(ctx As VstPluginContext)
    Dim noteOffset As Integer = 0
    Dim detune As Short = 0
    Dim Velocity As Integer = 127

    'Dim noteOn As New NAudio.Midi.NoteEvent(AbsoluteTime, note.MidiChannel, NAudio.Midi.MidiCommandCode.NoteOn, note.Note.BaseNote, Velocity)
    Dim noteOnStream As New System.IO.MemoryStream()
    Dim noteOnData As New System.IO.BinaryWriter(noteOnStream)
    'noteOn.Export(AbsoluteTime, noteOnData)
    noteOnData.Write(MidiMessage.StartNote(60, Velocity, 1).RawData)
    Dim noteOnEvent As New VstMidiEvent(0, 400, 0, noteOnStream.ToArray, detune, Velocity, True)
    vEvents.Add(noteOnEvent)

End Sub

End Class

redpajama_set_name: RedPajamaStackExchange


text:
A traitor is plotting to assassinate the President of the United States...and he's closer than anyone could imagine. Longtime Secret Service agent Pete Garrison (Michael Douglas) finds himself the prime suspect in the deadly scheme. With his former protege (Kiefer Sutherland) leading the manhunt to bring him in, Pete races to save the commander in chief and clear his name.
Starring: Michael Douglas, Kiefer Sutherland, Eva Longoria, Martin Donovan, Kim Basinger
WriterGeorge Nolfi, Gerald Petievich
DirectorClark Johnson
ProducerMichael Douglas, Marcy Drogin, Arnon Milchan, Bill Carraro
Jaws (HBO)
The Pacifier (HBO)
Battle for Terra (HBO)
The Trouble With Spies (HBO)
Astro Boy (HBO)
Pokemon Detective Pikachu (HBO)
Eragon (HBO)

redpajama_set_name: RedPajamaCommonCrawl


Although I really need to get in gear on that wooly winter coat, I wanted to do a few simple projects to get back in the swing of sewing, and I thought a few "instant gratification" tops would be good projects. I have been doing a lot of sewing for the sister, before she is gone for an extended period of time, and I decided to try out Simplicity 3842 on a top for her.
I really like both views of this top – I think they are both pretty cute. For my sister I made view B out of a purple plaid cotton knit (very stable, practically no stretch). The lace and bias binding on the neck were gifts from another sewer's stash (for which I don't believe I ever properly expressed my gratitude, but truly, I am eternally grateful), and the cotton was $2.50/yard, and I used only a little over a yard, so total cost of this shirt was definitely under $5.
Pattern Description: Tunic top in two styles. View A with long sleeves and longer bodice, view B with shorter sleeves and shorter length.
Pattern Sizing: (8-10-12-14-16-18). I really like that all sizes are included in one envelope.
Were the instructions easy to follow? Yes. The instructions were quite straightforward. The only tricky step is turning the loops for the ties. I have a loop turner, which actually worked on this fabric, so it wasn't too bad for me, but this could potentially be a major pain. Other than that the instructions are very simple, and the top is quick to make.
Did it look like the photo/drawing when you were done with it? Yes! It looked very much like the view B drawing, except for the colors. But the style of the shirt looked remarkably like the drawing.
What did you particularly like or dislike about the pattern? I really like the style of the top and the easy instructions. There aren't too many pieces. Also, the instructions include finishing details (like ribbon supports and bias binding) that help make the results more finished and better quality. As for dislikes – I think the B view top is simultaneously a bit low and a bit short. Normally, I do not make length corrections for my sister, but I think I would have added 3/4 inch of length just to make the top a bit less prone to rising up in the back. I did not hem the bottom as instructed because it would have been much too short. I would also add an extra inch to the top of the front inset piece. Looking at the model in the envelope photo, it looks a bit low there as well. I think for view A the length would be good (as the pattern is much longer) but the top would still need to be raised a bit.
Fabric used: Stable cotton knit. It has practically no stretch to it and was pretty cheap – about $2.50/yard.
Pattern alterations or design changes you made: None. Normally my sister fits into patterns out of the envelope fairly well (don't even have to mix sizes), but in this case I could have made a few changes (see the "dislikes" section) to make a better fit or more comfortable garment.
Would you sew it again? Would you recommend it to others? Yes to both questions! I think altering length and adding a bit to the top are minor alterations that can be easily done in the future. I would totally make this top again for my sister, and I would love to make both view A and B for myself as well. I think the results are really good considering how quickly this pattern can be sewn up. Overall I would say this pattern is highly recommended.
Conclusion: Great pattern! Although I think a few minor alterations would be necessary (raising the top a bit), this pattern produces some nice results without any major changes. The results are simple to obtain and the end product looks very finished. Overall, I really like it!
So sorry you found this post a waste of time. Perhaps if you left an actual question I could be of more assistance in answering it.
I was very thankful to find this pattern review. I am trying to sew the pattern and I don't understand the directions regarding using ribbon straps to connect the bodice insert. Can someone please shed some light on what I'm supposed to be doing. Obviously, I'm an active visual learner but couldn't find any YouTube videos on sewing this pattern.
Are you talking about the ties on this top? I think I either caught them in the seam or top stitched them in place; either method could work.
No, not the ties. The bodice has some kind of ribbon on the inside that seems to attach to the bodice inset. I can't figure out what they are trying to do. In my mind, it seems like the inset is just being held up by the ribbons and not sewn to the "V" of bodice?
I feel like I just ignored that part because it didn't make sense.


text:
Quidd: Digital Collectibles 12+
Buy. Sell. Collect.
Quidd Inc
4.0, 13.7K Ratings
Quidd is the world's largest marketplace for digital trading cards and more!
Remember trading cards? They're back, in digital form.
Build the ultimate collection by choosing the right mystery packs from hundreds of your favorite brands, shows, anime, movies, comic books, and games!
Join millions of fans who are chasing limited-edition digital stickers, digital trading cards, and digital 3D figures!
Be the first to own rare items and level up to become the ultimate fan with the most valuable collection!
-> Find brands you love, like Disney®, Rick & Morty, Game of Thrones, MARVEL, Transformers™, My Little Pony™, Naruto: Shippuden, and more
-> Open mystery packs and discover what's inside
-> Keep what you love and sell the rest for coins
-> Level up as your Collection Value grows
-> Become one of the best collectors in the world
With new sets dropping every day and over 2.1 BILLION individual items in circulation, you're sure to find something you love — and something valuable — for your collection.
You can also share the stickers that you collect with your friends on iMessage! We'll never track your keystrokes.
Are you ready to become the best collector? Join the Quidd community now!
There are over 100 brands to collect on Quidd, including:
Naruto: Shippuden
Courage the Cowardly Dog
Dexter's Laboratory
Dungeon's & Dragons
Ed, Edd, N' Eddy
The Grim Adventures of Billy and Mandy
Uncle Grandpa
OFFICIAL HBO LICENSED PRODUCT © 2018 HOME BOX OFFICE, INC. ALL RIGHTS RESERVED. HBO AND RELATED TRADEMARKS ARE THE PROPERTY OF HOME BOX OFFICE, INC.
ADULT SWIM, the logo, RICK AND MORTY, and all related characters and elements are trademarks of and © 2018 Cartoon Network. A Time Warner Company. All rights reserved.
©2018 Cryptozoic Entertainment. 25351 Commercentre Dr. Suite 250, Lake Forest, CA 92630. All rights reserved.
TM & © 2018 CBS Studios Inc. STAR TREK marks and logos are trademarks of CBS Studios Inc. All Rights Reserved.
Bob's Burgers™ & © 2018 Twentieth Century Fox Film Corporation. All Rights Reserved.
© 2018 MARVEL, Inc.
© 2018 Hasbro, Inc.
© 2018 Sanrio, Inc.
© 2018 The Walt Disney Company, Inc.
© 2018 VIZ MEDIA, Inc.
NEW! With improvements to our fandom stores, you'll be able to clearly see currently available, award, and Collector's Edition content as well as sort & filter sets to find exactly what you're looking for!
13.7K Ratings
L the Panda , 09/01/2018
Great, but..
Quidd is an awesome app it just has some quirks that make it sometimes annoying. (Reasons why it's awesome at the bottom) first of all the feature probably 80% of the people on quidd probably hate the special editions/ hyper shots/scattershot/etc..The idea that only a few people can get something super rare is cool but annoying. Special editions cost a lot of quidd coins and take forever to earn quidd coins for.(only takes a few days but still) and you can only by like less than half of the set and by the time you same enough coins for the rest of the set it's all sold out! The largest problem with quidd is the hypershots/scattershot/etc. you can usually only buy them with REAL Money for the set. Some of them make it so you have to buy a certain 100 card pack just to receive it meaning people can't buy because they either don't want to waste their money on something virtual or just 18 or younger (me) which is probably most people who can't purchase them. With all of these issues aside the basic quidd is really cool and fun Shelfies are semi interesting and the idea of being able to collect stickers of your favorite fandoms is awesome and being able to use them in iMessage is even cooler. If quidd didnt have the issues it did I would rate it 1 million at of 5 just without those stupid special edition/scattershot/hyper shots. I would give this app a 4 out of 5 stars
RecoveryGamesOfficial , 07/01/2019
Been here for 2+ Years
So I figured I might as well do a review. First off, don't listen to the people who say customer support is weak, because they are just upset. Customer support has gotten me my account back after an incident where someone reported me just to do so. The support is wonderful and really nice. They have lots of content, and Its super easy to use without paying so much money. Just need patience guys! I do like the new beta feature of selling, however I would like to post some suggestions regarding Quidd in general. So listen Quidd, my friend, you guys have Disney right? So why not Star Wars?!? Disney now owns the rights to it and I see it as a big game changer if you do. In the real world, Star Wars merchandise Sells quick!! So thats just a tip. Also, this next suggestion I spoke with the team about but I'd like to post it here. What if we have a verified users stamp? And maybe even a space to advertise for our shops other than listings? I mean, I am doing great with my shop, but like eventually business will slow down for me. I was selling 60+ items a day, to now like 20 a week. I went from 0 sales to 502 in just two weeks since I have been back! But now Its been days and barely a sale. I also recommend that we have more free options on the Fyber coin wall. I barely get those anymore and when I do, I take the offer asap! Anyways, thanks to those who read my rambling of ideas.
_zepster_ , 04/14/2018
It's fun but some issues
Alright so I just started a few days ago and I was thrilled to collect things. Of course in a way this is kind of dumb as you can't actually get these but collecting is still fun when it's digital. Anyways, since I started "late" all of the items that are here are sold out, which makes you needing to trade with people. There's no problem with trading things but sometimes people are at high demands for things you don't have. Another thing is that there should be more fandoms. There's just so little options and out in the real world, there are more movies, games and comic funko pop vinyl figures to choose. Just add a new fandom like The Walking Dead, or Stranger Things, it literally any other show or video game. Finally, the coin system. I'm not the one for buying in-game currency so I usually watch an ad to get 500 coins. But sometimes it doesn't want to give me the coins so I just wasted 30 seconds for no reason. I've watched 5 videos in a row and on the final try, I got my 500 coins and ONLY 500 coins. It didn't add up all the other times so I just got robbed of time. And one last and final thing is the showcase. Now I thought it would be a good idea to fill up a thing with pop vinyls. But ever since I added like 12 of them, the app just crashes over and over again. Maybe it's because the figures take up so much space but it's just ridiculous.
Any ways, it's still fun. It just needs some things tweaked and fixed
Quidd Inc.
© 2016-2018 Quidd Inc.
Direct Purchase - Tier 1A $0.99
Coins $4.99
Stack of Coins B $4.99
St Patrick's Day By Quidd Labs
Sushi Stickers by Quidd Labs
WOW Pixel - Live Wallpapers
Celebrity Voice Changer - Face
WEBTOON - Find Yours
Cartoon Network App


text:
Q: proceso se detiene al pasarlo a segundo plano hola tengo un programa que tiene un proceso muy pesado durante el cual se muestra una barra de progreso. El problema es que cuando paso el programa a segundo plano (utilizando el boton redondo de android) la barra de progreso se detiene. Luego cuando paso la aplicacion a primer plano otra vez, vuelve a reanudarse. Entonces queria saber si hay algun modo de que la app no se detenga al pasarla a segundo plano. Por cierto ya he desactivado el "Ahorro de bateria en aplicaciones" y sigue igual. El codigo que muestro es una version minima de mi programa real, donde se puede reproducir la situacion.
Un saludo.
public class MainActivity extends AppCompatActivity {
    private ProgressBar progressBar;
    Button btn;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        btn = (Button) findViewById(R.id.btn);
        progressBar=findViewById(R.id.progressBar);
        progressBar.setMax(10000000);
        btn.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                new MyTask().execute(10);
            }
        });
    }
    class MyTask extends AsyncTask<Integer, Integer, String> {

        @Override
        protected String doInBackground(Integer... params) {

            for(int i=0;i<10000000;i++)
            {
                progressBar.setProgress(i);
            }

            return "Task Completed.";
        }

        @SuppressLint("WrongThread")
        @Override
        protected void onProgressUpdate(Integer... values) {
            //txt.setText("Running..."+ values[0]);
            progressBar.setProgress(values[0]);

        }

    }
}


text:
Prionobelum durum är en mångfotingart som beskrevs av Karl Wilhelm Verhoeff 1924. Prionobelum durum ingår i släktet Prionobelum och familjen Zephroniidae. Utöver nominatformen finns också underarten P. d. nitidum.

Källor

Dubbelfotingar
durum

redpajama_set_name: RedPajamaWikipedia


An anthology series centered around some of history's most famous criminals, including O.J. Simpson.
watch American Crime Story online free. American Crime Story streaming tv show, Full Episode. tv series online.


text:
NFL Awards Betting Update
By Josh Appelbaum (VSIN.com) Follow @josh_insights
Today bettors have a loaded Friday slate to choose from, including 9 NBA games, 2 NHL games and 12 College Basketball games. For an updated breakdown of Thursday's betting action, be sure to tune in to the VSiN Market Insights Podcast with Josh Appelbaum. It will be posted by 2:30 p.m. ET.
I'll be joining The Lombardi Line at 1:30 p.m. ET to offer a market update and then I'll be co-hosting Betting Across America with Mike Pritchard from 3 to 4 p.m. ET.
In the meantime, let's update the NFL Awards market heading into Week 18. For many bettors, this is their last chance to cash a ticket before the lines skyrocket and then go off the board.
Midway through the season this was Tom Brady's award to lose. And it appears he will lose out to Aaron Rodgers. The Packers QB is a -400 favorite to win MVP entering the final weekend. Rodgers is receiving 8.2% of tickets but 21.3% of the money at BetMGM. Rodgers has guided Green Bay to the 1-seed and the best record in the NFL. Brady has thrown for more yards (4,990 vs 3,977) and touchdowns (40 vs 35). But Rodgers has thrown fewer interceptions (4 vs 12) and has a higher rating (111.1 vs 100.5).
Much like the MVP, this award was ticketed to Patriots QB Mac Jones for much of the year. But Bengals WR Ja'Marr Chase just overtook Jones and is now a -225 favorite. Chase was as high as 500 entering Week 17 but then he dazzled with 11 catches, 266 yards and 3 touchdowns against Kansas City and has since flipped to the favorite. Chase now sits at 70 catches, 1,429 yards and 13 touchdowns on the season. Chase is receiving 18.3% of tickets but 31.1% of money. One wonders if the voters will be biased against Jones (now 185) due to the fact that he landed in the best situation with a stable franchise and great coaching.
This is the most interesting award to bet on because it's a literal coin flip between the best wide receiver and the best running back. Rams WR Cooper Kupp and Colts RB Jonathan Taylor are both co-favorites at -110. Kupp leads the NFL with 138 catches, 1,829 yards and 15 touchdowns, the vaunted "triple crown." Meanwhile, Taylor has rushed for 1,734 yards and 18 touchdowns, including a 5.5 average. Taylor is receiving 15.7% of the tickets but only 14.3% of the money, which means his support is likely public money. However, Kupp is receiving only 7.5% of tickets but 22.2% of the money. That pronounced "low bets, higher dollars" bet split signals quiet yet bold sharp money on Kupp to win the award.
Steelers edge rusher T.J. Watt has separated from the pack and is now a -400 favorite to win the award. Watt leads the NFL with 21.5 sacks. The next closest player in Robert Quinn with 18 sacks. Watt is receiving 22% of bets but a whopping 48.7% Of the handle, a massive smart money discrepancy. As high as the -400 seems, it still might be worth laying it. Micah Parsons has the next best odds at 350 but he was just placed in COVID protocol and could miss the finale. Watt is 180 to break the record for sacks (Strahan has 22.5). He would need 1.5 sacks in the finale against the Ravens.
Comeback Player of the Year
Cowboys QB Dak Prescott was the favorite to win the award all season and remains the favorite at -200. But the gap has shortened thanks to late steam hitting Bengals QB Joe Burrow ( 105). Prescott is receiving 22.7% of tickets but 25.3% of the handle. Meanwhile, Burrow is receiving 20.8% of bets but 53.4% of the handle, a sharper bet split. Burrow has the higher completion percentage (70.4 vs 68.4), more touchdowns (34 vs 32), more yards (4,611 vs 4,154) and a higher QB rating (108.3 vs 100.9). Burrow won't play in the finale. But with better numbers and late movement in his favor he may be worth a look at 105.
Similar to the Offensive Rookie of the Year, this award is a coin flip between two coaches. Zac Taylor of the Bengals and Matt Lafleur are both co-favorites at 160. Mike Vrabel of the Titans is 350 but receiving the most tickets (18.2%). While Lafluer has lead Green Bay to the best record in the NFL, voters may hold it against him that he has Aaron Rodgers. After all, any coach would look great if Rodgers was their quarterback. On the flip side, Taylor has received a lot of late action. Historically, this award has gone to a coach who takes a bad team and flips them into a good team. The Bengals went 4-11-1 last season and are now 10-6 and won the division. That rags to riches success story typically brings this award home.
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text:
Addict Gaming
Online Video Game
Earning Games
Football World Cup
Women Sports
Home Rugby
'Smartest team within the global': New rugby boss' Wallabies ambition
by Alfonso Murray
in Rugby
It's a capture phrase that ultimately was given misplaced in translation for the duration of Malcolm Turnbull's top ministership, however, Scott Johnson wants Australian rugby to yet again be the innovators and re-setup itself because of the "smartest" kingdom in the global.
At the flip of the century, whilst the Wallabies were sweeping every person earlier than them, Australian rugby changed into recognized for its first-rate innovation.
The Brumbies redefined the tackle technique and defensive systems within the late Nineties and by means of doing so were capable of getting in front of oppositions with the aid of figuring out the satisfactory manner to counteract them.
It led the Brumbies to 2 Super Rugby titles early in the twenty-first century and the Wallabies, with playmakers George Gregan and Stephen Larkham pulling the strings, received their 2d World Cup and defeated the British and Irish Lions too.
And on the eve of the 2019 World Cup, which has been proceeded by means of greater than a decade of inconsistent and underwhelming results, Rugby Australia's newly appointed director of rugby wants the country to get lower back to what it turned into previously recognized for.
"What I assume Australia desires to be and wants to be is a skillful crew, play attractive rugby and are taken into consideration the smartest," Johnson said in a wide-ranging interview on Fox Sports' Super Saturday.
"I turned into lucky to go through a coaching pathway that Australia became constantly famed on the sector level as the smart ones. We didn't have the most important, it wasn't our most important game, so we competed in opposition to numerous groups, but we were continually taken into consideration the clever team.
"We want to educate our children within the academies that we want the acumen, we want the obligation, we want the self-rely and care. To do this and the sport we need to play we need legs, we want miles in our legs and we want to run speedily for longer, skills, acumen and pace and endurance, that's what I need and that's in which we want to complete, and I suppose anyone will agree if we get that at the sporting panorama Australian rugby could be nicely respected and I'd want to be taken into consideration the best kingdom within the international."
Johnson, who changed into the Wallabies' attack teach on the 2007 World Cup in-among lengthy stints in Wales and Scotland, stated the lack of influential coaches had hurt the game in Australia however changed into optimistic with the emerging skills coming through.
"I assume what we got, we misplaced a whole lot of highbrow property in a quick time frame," Johnson said.
"We've were given surely appropriate coaches coming thru our system. The coaches in the provincial teams are truly right high-quality coaches, however, we've misplaced a whole lot of human beings at one technology and so the highbrow belongings left, (we're) seeking to drain it again.
"And that's what's encouraging having seen your coaches at the more youthful stage and, consequently, placing the onus on the children at a younger age. It's simply not at the provincial stage, it's at the younger degree as well. We need those more youthful players coming through nicely educated, properly versed, well-knowledgeable on the sport and, therefore, just now not paying attention to observation, know-how the game, arising with creative thoughts to play, it shouldn't just be about the teaching, if we're all aligned that way, we'll be a fascinating u . S. To look at and that's my ambition."
Alfonso Murray
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text:
Is a prototype website created during the 2017 United Way Hackathon. The main purpose of the application was to bridge gaps between communities by introducing food as a common theme.

## To Run Site

1. [Install Node.js][]
+ cd into this project's root directory
+ Run `npm install` to install the app's dependencies
+ Run `npm start` to start the app
+ Access the running app in a browser at <http://localhost:6001>

[Install Node.js]: https://nodejs.org/en/download/

redpajama_set_name: RedPajamaGithub


text:
package org.carlspring.strongbox.configuration;

import org.carlspring.strongbox.yaml.YAMLMapperFactory;
import org.carlspring.strongbox.yaml.YamlFileManager;
import org.carlspring.strongbox.yaml.repository.CustomRepositoryConfigurationDto;
import org.carlspring.strongbox.yaml.repository.remote.RemoteRepositoryConfigurationDto;

import javax.inject.Inject;

import org.springframework.beans.factory.annotation.Value;
import org.springframework.core.io.Resource;
import org.springframework.stereotype.Component;

/**
 * @author Przemyslaw Fusik
 */
@Component
public class ConfigurationFileManager
        extends YamlFileManager<MutableConfiguration>
{
    @Value("#{@propertiesPathResolver.resolve('strongbox.config.file','etc/conf/strongbox.yaml')}")
    private Resource resource;

    @Inject
    public ConfigurationFileManager(YAMLMapperFactory yamlMapperFactory)
    {
        super(yamlMapperFactory, CustomRepositoryConfigurationDto.class, RemoteRepositoryConfigurationDto.class);
    }

    @Override
    protected Resource getResource()
    {
        return resource;
    }
}


text:
\section{Introduction}

Let $A \in \mathbb{Z}^{m\times n}$ with $\rank(A) = m$, $c \in \mathbb{Z}^n$, and $b \in \mathbb{Z}^m$.
For $k \in \{1, \dotsc, m\}$, denote the largest absolute value of a minor of order $k$ of the matrix $A$ by
\[
\Delta_k := \Delta_k(A) := \max \{|\det(B)| : B \text{ is a } k \times k \text{ submatrix of } A\}.
\]
Note that $\Delta_1 = \|A\|_{\infty}$ is the largest absolute entry of $A$. For simplicity, we set $\Delta:=\Delta_m$.

We consider the standard form integer program
\begin{equation}\label{IP}
\max\{c^\transpose z : Az = b, ~  z \in \mathbb{Z}^n_{\ge 0} \} \tag{\text{IP}}
\end{equation}
and its linear relaxation
\begin{equation}\label{LP}
\max \{ c^\transpose x :  Ax =  b, ~ x \in \mathbb{R}^n_{\ge 0}\} \tag{\text{LP}}.
\end{equation}
Throughout, we assume that~\eqref{IP} is both feasible and bounded.

Given an optimal vertex solution $x^*$ to~\eqref{LP}, we investigate the question of~\eqref{LP} to~\eqref{IP} proximity: can we bound the distance from $x^*$ to some optimal solution $z^*$ of~\eqref{IP}?
We refer to any bound $\tau$ on $\|x^* - z^*\|_1$ as a \emph{proximity bound}.
Proximity bounds have a variety of implications in the theory of integer programming.
For example, a proximity bound of $\tau$ translates into a bound of $\tau \cdot \|c\|_{\infty}$ on the so-called integrality gap~\cite{CooSens,GraProx,HochConv}.
Furthermore, strong proximity bounds reduce the time needed for a local search algorithm to find an optimal~\eqref{IP} solution starting from an optimal~\eqref{LP} solution~\cite{WeiProx}.

One of the first seminal results on proximity is by Cook et al.~\cite{CooSens}, who established that there exists an optimal solution $z^*$ to~\eqref{IP} satisfying

\begin{equation}\label{eqCookBound_infty}
\|z^* - x^*\|_\infty \le n \cdot \max\{\Delta_{k} : k \in \{1, \dotsc, m\}\} .
\end{equation}
Cook et al. actually consider problems in inequality form, i.e., with constraints $Ax \le b$ rather than $Ax = b$, but their results easily translate to the standard form setting.
 A closer analysis reveals that $\Delta$ suffices for the standard form problem rather than $\max\{\Delta_{k} : k \in \{1, \dotsc, m\}\} $ stated in~\eqref{eqCookBound_infty}.
 %
Furthermore, if we naively extend~\eqref{eqCookBound_infty} to a bound on proximity in terms of the $\ell_1$-norm, then we obtain $\|z^* - x^*\|_1 \le n^2\Delta$.
Another closer analysis
gives us the bound
\begin{equation}\label{eqCookBound}
\|z^* - x^*\|_1 \le (m+1)n\Delta.
\end{equation}
See the proof of Lemma~\ref{MixedProx} for the two `closer analyses' referred to above.
Cook et al.'s bound has been generalized to various problems including those with separable convex objective functions~\cite{GraProx,HochConv,WerSep} or with mixed integer constraints~\cite{paat2018distances}, and extended to alternative data parameters such as $k$-regularity~\cite{Lee_LAAsubspaces,LeeRegu} and the magnitude of Graver basis elements~\cite{eisenbrand2019algorithmic}.

Notice that the proximity bound in~\eqref{eqCookBound} depends on the dimension.
In 2018, Eisenbrand and Weismantel~\cite{WeiProx} proved that proximity can be bounded independently of the dimension by establishing the bound
\begin{equation}\label{eqEWEntryBound}
\|z^* - x^*\|_1 \le m(2m\cdot \|A\|_{\infty}+1)^m.
\end{equation}
The proof of~\eqref{eqEWEntryBound} involves the Steinitz Lemma~\cite{S1913}.
By applying a different norm in the Steinitz Lemma, Eisenbrand and Weismantel's result can be restated as
\begin{equation}\label{eqEWDeltaBound}
\|z^* - x^*\|_1 \le m(2m+1)^m\cdot \Delta.
\end{equation}
The proximity bounds~\eqref{eqEWEntryBound} and~\eqref{eqEWDeltaBound} also hold for standard form problems with additional upper bound constraints on the variables.

As for lower bounds on proximity, it is not difficult to come up with examples demonstrating $\|z^* - x^*\|_1 \ge m \cdot \Delta$ and $\|z^* - x^*\|_1 \ge \|A\|_{\infty}^m$.
Aliev et al.~\cite{AHO2019} give a tight lower bound $\Delta-1$ on proximity in terms of the $\ell_\infty$-norm when $m = 1$.
However, it remains an open question if \eqref{eqCookBound}, \eqref{eqEWEntryBound}, or \eqref{eqEWDeltaBound} is tight in general.
To this end, Oertel et al. established that the upper bound $\|z^* - x^*\|_1 \le (m+1) \cdot (\Delta-1)$ holds for most problems, where `most' is defined parametrically with $b$ treated as input~\cite{OPW2020}.

\subsection{Statement of Results and Overview of Proof Techniques}

The focus of this paper is to create stronger proximity bounds.
Recall that $\Delta := \Delta_m$.
Our first main result is an improvement over~\eqref{eqEWDeltaBound} for fixed $\Delta$.
We always consider the logarithm $\log(\cdot)$ to have base two.
\begin{thm}\label{DeltaProx}
For every optimal \eqref{LP} vertex solution $x^*$, there exists an optimal \eqref{IP} solution $z^*$ such that
\[
\|z^* -x^*\|_1 <3m^2 \log (2\sqrt{m}\cdot \Delta^{1/m}) \cdot \Delta.
\]
\end{thm}
Theorem~\ref{DeltaProx} demonstrates that proximity in the $\ell_1$-norm between~\eqref{IP} solutions and~\eqref{LP} \emph{vertex} solutions is bounded by a polynomial in $m$ and $\Delta$.
We focus on vertex solutions because proximity may depend on $n$ for general non-vertex~\eqref{LP} solutions.
For example, suppose that $c = 0$ and take any feasible solution to~\eqref{LP}, which is optimal in this case, such that each of the $n$ components is in $\sfrac12+\mathbb{Z}$.

Our second main proximity result is in terms of $\|A\|_{\infty}$ \emph{after $A$ is transformed by a suitable unimodular matrix}.
Recall that a unimodular matrix $U \in \mathbb{Z}^{m\times m}$ satisfies $|\det(U)| = 1$, so the $m\times m$ minors of $UA$ have the same magnitudes as those of $A$.
Moreover, the optimal solutions of~\eqref{IP} are the same as the optimal solutions to
\begin{equation}\label{eqUIP}
\max\{c^\transpose z : UAz = Ub, ~ z \in \mathbb{Z}^n_{\ge 0}\}.\tag{$U$ - IP}
\end{equation}
If we know an $m \times m$ submatrix $B$ of $A$ satisfying $|\det(B)| = \Delta$, then in polynomial time we can find a unimodular matrix $U$ such that $UB$ is upper triangular, which implies that $\Delta \leq \|UB\|_\infty ^m$.
Here, we can apply Theorem~\ref{DeltaProx} to obtain the bound
\begin{equation}\label{eqLargestHNF}
\|z^* -x^*\|_1 <3m^2 \log (2\sqrt{m}  \cdot \|UB\|_\infty )\cdot \|UB\|_\infty ^m.
\end{equation}

The previous bound is predicated on the knowledge of an $m \times m$ submatrix of maximum absolute determinant, which is NP-hard to find~\cite{K1995}.
However, Di Summa et al.~\cite{SumSubdet} established that this submatrix can be approximated in polynomial time.
In particular, they demonstrated that there exists an $m \times m$ submatrix $B$ of $A$ satisfying
\begin{equation}\label{eqDetApprox}
\Delta \le |\det(B)| \cdot (2\log(m+1))^{m/2}
\end{equation}
that can be found in time polynomial in $m$ and $n$.\footnote{The approximation result of Di Summa et al. involves an $\epsilon$ factor of precision and the running time is polynomial in $m,n,1/\epsilon$. For the sake of presentation, we have fixed this $\epsilon$ to $1/m$ and obtain a polynomial time algorithm in $m,n$.}
Similarly to the above, there exists a unimodular matrix $U \in \mathbb{Z}^{m\times m}$ for which $UB$ is upper triangular that can also be found in polynomial time.
We can use this approximate largest absolute determinant to derive our second main result.
We denote the linear relaxation of~\eqref{eqUIP} by ($U$ - LP).
\begin{thm}\label{eqThmEntry}
Let $B$ be an $m\times m$ submatrix $B$ of $A$ satisfying~\eqref{eqDetApprox} and $U \in \mathbb{Z}^{m\times m}$ a unimodular matrix such that $UB$ is upper triangular.
Then for every optimal \textnormal{($U$ - LP)} vertex solution $x^*$, there exists an optimal \eqref{eqUIP} solution $z^*$ satisfying
\[
\|z^* -x^*\|_1 <3m^2 \log (2\sqrt{2m\log (m+1)} \cdot \|UB\|_\infty  )  \cdot (2\log (m+1))^{m/2}\cdot \|UB\|_\infty ^m.
\]
\end{thm}
It is worth reemphasizing that the proximity bound in Theorem~\ref{eqThmEntry} can be determined in polynomial time, which is in contrast to the bound in~\eqref{eqLargestHNF}, and the dependence on $m$ is significantly less than the bound in~\eqref{eqEWEntryBound}.

The proofs of Theorems~\ref{DeltaProx} and~\ref{eqThmEntry} are based on combining proof techniques of Cook et al.~\cite{CooSens} with results on the sparsity of optimal solutions to~\eqref{IP}.
The \emph{support} of a vector $x \in \mathbb{R}^n$ is defined as
\[
\supp(x) := \{i \in \{1, \dotsc, n\} : x_i \neq 0\}.
\]
A classic theorem of Carath\'eodory states that $|\supp(x^*)| \le m$ for every optimal vertex solution of~\eqref{LP}.
It turns out that the minimum support of an optimal solution to~\eqref{IP} is not much larger.
Denote the minimum support of an optimal solution of~\eqref{IP} by
\[
S := \min\left\{|\supp(z^*)| :
z^* \text{ is an optimal solution for~\eqref{IP}}
\right\}.
\]
Aliev et al.~\cite{ADEOW2018} established that
\begin{equation}\label{eqSparseSolution}
S \le m+\log\left(\sqrt{\det(AA\strut^{\transpose})}\right) \le  2m\log(2\sqrt{m} \cdot \|A\|_{\infty}).
\end{equation}
For other results regarding sparsity, see~\cite{ADOO2017,ES2006,OPW2019} for general $A$ and~\cite{BG2004,BrunsGHMW1999,CookFS1986,Sebo1990} for matrices that form a Hilbert basis.
See also the manuscript of Aliev et al.~\cite{AADO2019}, who give improved sparsity bounds for \emph{feasible solutions} to special classes of integer programs and provide efficient algorithms for finding such solutions.
Using sparsity, we derive the following proximity bound which forms the basis for Theorems~\ref{DeltaProx} and~\ref{eqThmEntry}.

\begin{lem}\label{MixedProx}
For every optimal \eqref{LP} vertex solution $x^*$, there exists an optimal \eqref{IP} solution $z^*$ such that
\[
\| z^* -x^* \|_1 < (m+1)\cdot(m+S)\cdot \Delta.
\]
\end{lem}

Lemma~\ref{MixedProx} improves~\eqref{eqCookBound} by replacing the dependence on the dimension $n$ to $m+S$.
Lemma~\ref{MixedProx} is stated for a generic sparsity bound, so one could use it together with~\eqref{eqSparseSolution} to achieve a proximity bound in terms of $\Delta$ and $\|A\|_{\infty}$.
In order to provide a bound for proximity that is uniform in the data parameter, we prove a new sparsity result in terms of $\Delta$.
\begin{thm}\label{DeltaSpars}
There exists an optimal \eqref{IP} solution $z^*$ such that
\begin{equation*}
|\supp (z^*)|< 2m\log \bigl(\sqrt{2m} \cdot \Delta^{1/m}\bigr).
\end{equation*}

\end{thm}

\smallskip

Our proximity bounds can be generalized to mixed integer programs.
Given an index set $\mathcal{I} \subseteq \{1, \dotsc, n\}$, the mixed integer program with integrality constraints indexed by $\mathcal{I}$ is
\begin{equation}\label{MIP}
    %
    \max\{c^\transpose z : Az = b, ~  z\ge0, ~ z_i \in \mathbb{Z} ~\forall~i\in\mathcal{I} \}. \tag{\text{MIP}}
    %
\end{equation}
Similarly to~\cite[Corollary 4]{ADEOW2018}, we establish the extension of Theorem \ref{DeltaSpars} to \eqref{MIP}.
\begin{cor}\label{DeltaSparsMIP}
    There exists an optimal \eqref{MIP} solution $z^*$ satisfying
    %
    \begin{equation*}
    |\supp (z^*)|< m+2m\log \bigl(\sqrt{2m}\cdot \Delta^{1/m}\bigr)=2m\log \bigl(2\sqrt{m}\cdot \Delta^{1/m}\bigr).
    \end{equation*}

\end{cor}

We obtain the following proximity result by applying Corollary \ref{DeltaSparsMIP}.
 %
\begin{cor}\label{DeltaProxMIP}
    %
    For every optimal \eqref{LP} vertex solution $x^*$, there exists an optimal \eqref{MIP} solution $z^*$ such that
    %
    \[
    \|z^* -x^*\|_1 <3m^2 \log (2\sqrt{2m}\cdot \Delta^{1/m}) \cdot \Delta.
    \]
\end{cor}

Our results also extend to integer programs in general form.
Let $A\in\mathbb{Z}^{m \times n}$ and $B\in\mathbb{Z}^{m \times d}$ be matrices satisfying $\rank ([A, B])=m$.
Note that it is not necessary to assume that $\rank(A) = m$ in our general form results.
Let $C\in\mathbb{Z}^{t \times d}$, $c \in \mathbb{Z}^{n+d}$, $b_1 \in \mathbb{Z}^m$, and $b_2 \in \mathbb{Z}^{t}$.
The \emph{general form integer program} is
\begin{equation}\label{GIP}
\max \left\{c^\transpose z  :
\begin{array}{rcl}
[A,~ B]~z  & = &  b_1\\[.15 cm]
[{0},~C]~z  & \le & b_2
\end{array},
~~z \in \mathbb{Z}^{n+d},
~~z_i \ge 0~\forall ~i \in \{1, \dotsc, n\}
\right\}.
\tag{GIP}
\end{equation}
We define the general form linear program~(GLP) similarly.
Previously cited bounds on proximity hold for~\eqref{GIP}.
However, our analysis reveals that proximity for~\eqref{GIP} depends on the potentially smaller data parameter
\[
\delta := \max \left\{|\det(E)| :
\begin{array}{l}
E \text{ is any submatrix of } \begin{pmatrix} A & B \\ 0 & C\end{pmatrix} \\[.25 cm]
\text{ defined using the first } m \text{ rows}
\end{array}
\right\}.
\]
If $t =0$ and $d=0$, then~\eqref{GIP} is a standard form problem and $\delta = \Delta_m(A)$.
If $m =0$ and $n=0$, then~\eqref{GIP} is an inequality form problem and $\delta = \max\{\Delta_k(C) : k \in \{1, \dotsc, d\}\}$.
\begin{cor}\label{corProxPlusSparsity}
For every optimal \textnormal{(GLP)} vertex solution $x^*$, there exists an optimal \eqref{GIP} solution $z^*$ such that
\[
\|z^* -x^* \|_1 < \min \{ m+t+1,n+d \}\cdot  \Bigl(\min \bigl\{ n,2m \cdot \log (2\sqrt{m} \cdot \delta^{1/m}) \bigr\} +d\Bigr)\cdot  \delta .
\]
\end{cor}
The proximity bound in Corollary~\ref{corProxPlusSparsity} coincides with the best known bounds in both the standard setting and the inequality form setting.

Going beyond integer linear optimization problems, it would be ideal for proximity bounds in terms of sparsity to extend to integer programs with separable convex objective functions (see~\cite{GraProx,HochConv} for similarities between the linear and separable convex setting).
However, for separable convex \emph{maximization problems}, strong proximity bounds do not exist for exact solutions, in general, even though sparsity results apply.
In contrast, for separable convex \emph{minimization problems}, strong sparsity bounds do not exist for exact solutions, in general, even though the classic proximity techniques apply.

In the remainder of this paper, we provide the proofs of our results. In Section \ref{sec:sparsity}, we first present our proofs of the proximity bound derived from a generic sparsity bound (Lemma~\ref{MixedProx}) and the novel sparsity bound (Theorem~\ref{DeltaSpars} and Corollary~\ref{DeltaSparsMIP}), because the proofs of the proximity results depend on these.
Then in Section \ref{sec:proximity},  we
provide the proofs of the proximity results for the standard form integer programs (Theorem~\ref{DeltaProx} and Theorem~\ref{eqThmEntry}). The proof of the mixed integer case (Corollary~\ref{DeltaProxMIP}) is omitted because it is the same as the proof of the pure integer case except that a different sparsity bound is applied. Additionally, we provide a proof of the proximity result in the general form setting (Corollary~\ref{corProxPlusSparsity}).

\section{Proofs regarding sparsity}\label{sec:sparsity}

Given $A \in \mathbb{R}^{m \times n}$ and $I \subseteq \{1, \dotsc, n\}$, we let $A_I \in \mathbb{R}^{m \times |I|}$ denote the columns of $A$ indexed by $I$.
If $I = \{i\}$ for some $i \in \{1, \dotsc, n\}$, then $A_i := A_{I}$.
Similarly, given $u \in \mathbb{R}^n$, we let $u_I \in \mathbb{R}^{|I|}$ denote the components of $u$ indexed by $I$.

\begin{proof}[of Lemma~\ref{MixedProx}]
We prove the result by projecting the optimization problems onto the union of the supports of $x^*$ and an optimal~\eqref{IP} solution with minimal support.
 Let $\bar{z}  \in\mathbb{Z}^{n}_{\ge 0}$ be an optimal \eqref{IP} solution with minimum support.
 %
 By the definition of $S$ we have $|\supp (\bar{z})|= S$.
 %
 As $x^*$ is an optimal vertex solution of \eqref{LP}, we also have $|\supp (x^*)| \le m$.
 %
 Define
 %
 \[
 H :=  \supp (x^*) \cup \supp (\bar{z}),
 \]
 %
 and note that
 %
 \begin{equation}\label{eqDefnH}
 |H| = |\supp(x^*) \cup \supp (\bar{z})|\le |\supp(x^*) | +  |\supp(\bar{z}) | \leq m+S.
 \end{equation}
 %
If $n=m$, then $A$ is invertible and there exists a unique solution $A^{-1}b$ to the system $Ax = b$.
In this case $x^* = \bar{z} = A^{-1}b$.
Therefore, $\|x^* - \bar{z}\|_1 = 0$.
For the rest of the proof, we assume that $n>m$ and $H=\{ 1,\dots ,|H| \}$.

Consider the optimization problems

\begin{equation}\label{IP2}
\max \big\{ c_H^\transpose z : A_H z   =  b ,~ z   \in \mathbb{Z}^{|H|}_{\ge 0}\big\} \tag{IP2}
\end{equation}
and
\begin{equation}\label{LP2}
\max \big\{ c_H^\transpose x : A_Hx    =  b,~ x   \in  \mathbb{R}^{|H|}_{\ge 0} \big\}. \tag{LP2}
\end{equation}
Observe that $x^*_H$ is an optimal basic feasible solution for~\eqref{LP2}, and $\bar{z}_H$ is an optimal solution for~\eqref{IP2}

Rewrite \eqref{LP2} in inequality form as follows:
\[
\max\big\{ c_H^\transpose x   : A_Hx =b, -I_Hx \le 0,~x \in\mathbb{R}^{|H| } \big\},
\]
where $I_{H}$ is the $|H|\times |H|$ identity matrix.
Partition the rows of $-I_H$ into $D_1$ and $D_2$ such that $D_1 \bar{z}_H < D_1 x^*_H  $ and $D_2 \bar{z}_H \geq D_2 x^*_H $.
Define the polyhedral cone
\begin{equation}\label{eqCone}
K:= \left\{ u\in\mathbb{R}^{|H| }  :  A_H u = 0, ~ D_1 u \le 0, ~D_2 u \ge 0\right\}.
\end{equation}
Observe that $\bar{z}_H - x^*_H \in K$.

The cone $K$ is pointed because the submatrix defined by $D_1$ and $D_2$ in~\eqref{eqCone} has rank $|H|$.
Thus, there exists a set $U:=\{u^1, \dotsc, u^t\} \subseteq \mathbb{R}^{|H|} \setminus\{0\}$ that generates the extreme rays of $K$, i.e.,
\[
K = \bigg\{\sum_{i=1}^t \lambda_i u^i : \lambda_i \ge 0 ~ \forall ~ i \in \{1, \dotsc, t\}\bigg\}
\]
and $u^i$ satisfies $|H|-1$ linearly independent constraints in~\eqref{eqCone} at equality for each $i \in \{1, \dotsc, t\}$.

\begin{CLAIM}\label{claimExtRays}
For each $\tilde{u} \in U$ we have
\begin{equation}\label{eqExtRaySupp}
|\supp(\tilde{u})| \le m+1 .
\end{equation}
Also, each $\tilde{u}\in U$ can be scaled to have integer components and satisfy $\|\tilde{u}\|_{\infty}\le \Delta$.
\end{CLAIM}
\begin{proof}
Set $T:=\supp(\tilde{u})$ and without loss of generality assume $T =\{ 1,\dots ,|T|\}$.
Recall that $\tilde{u}$ satisfies a set of $|H|-1$ linearly independent constraints in~\eqref{eqCone} at equality.
One such set is composed of $|H|-|T|$ constraints from the system $D_1 \tilde{u} \le 0, ~ D_2 \tilde{u} \ge 0$ and $|T|-1$ constraints from $0=A_H\tilde{u}=A_T\tilde{u}_T$.
By this choice of constraints, it follows that
\[
|\supp(\tilde{u})| = |T| \le m+1
\]
and $|T| - 1 \le \rank(A_T) \le \min\{|T| ,m \}$.
Recalling $n > m$ and $\rank(A) = m$, the latter inequalities imply that there exists an index set $\overline{T}$ satisfying $T \subseteq \overline{T} \subseteq \{1, \dotsc, n\}$, $A_{\overline{T}} \in  \mathbb{Z}^{m\times (m+1)}$ and $\rank (A_{\overline{T}}) = m$.

Let $\bar{u} \in \mathbb{R}^{m+1}$ denote the vector obtained by appending $m+1-|T|$ zeros to $\tilde{u}_T$.
There exists an index set $I \subseteq \overline{T}$ with $|I| = m$ and $A_I$ invertible.
Let $i$ denote the singleton in $\overline{T} \setminus I$.
Because $A_{\overline{T}} \bar{u} = 0$, we have
\[
A_I \bar{u}_I = - A_i \bar{u}_i.
\]
If $\bar{u}_i = 0$, then $\bar{u} = 0$ and so $\tilde{u} = 0$.
However, this contradicts that $\tilde{u} \in U$.
Hence, $\bar{u}_i \neq 0$.
Scale $\bar{u}$ such that $|\bar{u}_i|=|\det ({A}_I)|$.
Applying Cramer's rule demonstrates that
\[
|\bar{u}_j| = |\det(A_{I \cup \{i\} \setminus \{j\}})| \qquad \forall ~ j \in I.
\]
Hence, $\bar{u}$, and consequently $\tilde{u}$, can be scaled to have integer components with $\|\tilde{u} \|_\infty  \leq\Delta$.
This proves the claim.
\qed
\end{proof}
For the rest of the proof, we assume that each $\tilde{u} \in U$ is scaled such that the conclusions of Claim~\ref{claimExtRays} hold.

Recall $\bar{z}_H -x^*_H \in K$.
By Carath\'eodory's theorem, there exists an index set $I\subseteq \{ 1,\dots , t \}$ with $|I| =|H|$ and $\lambda_i \in \mathbb{R}_{\ge 0}$ for each $i\in I$ such that

\[
  \bar{z}_H -x^*_H=\sum_{i\in I } \lambda_i u^{i} .
\]
Set $w := {\sum_{i\in I}} \lfloor\lambda_i \rfloor u^{i}$.
Using standard techniques in proximity proofs, it can be verified that $\tilde{z}:= \bar{z}_H -
$ is a feasible solution to \eqref{IP2}, and $\tilde{x}:= x^*_H+
$ is a feasible solution to \eqref{LP2} (see, e.g.,~\cite[Theorem 1]{CooSens}).
Moreover,
\begin{equation}\label{eqProjectedObjective}
 c^\transpose_H \bar{z}_H+c^\transpose_H x^*_H= c^\transpose_H \tilde{z}+ c^\transpose_H \tilde{x} .
\end{equation}
Because $x^*_H$ is optimal for~\eqref{LP2}, we have $c_H^\transpose\tilde{x}\le c_H^\transpose x^*_H$.
Combining this with~\eqref{eqProjectedObjective} proves that $c_H^\transpose \tilde{z}\ge c_H^\transpose \bar{z}_H$.
Because $\bar{z}_H$ is optimal for~\eqref{IP2}, we have $c_H^\transpose \tilde{z}= c_H^\transpose \bar{z}_H$ and  $\tilde{z}$ is also an optimal solution to \eqref{IP2}.

Define $z^* \in \mathbb{Z}^n_{\ge 0}$ component-wise to be
\[
z^*_i := \begin{cases} \tilde{z}_i &\text{if } i \in \{1, \dotsc,  |H| \}\\ 0 &\text{otherwise}.\end{cases}
\]
By construction $z^*$ is an optimal solution to~\eqref{IP} because $Az^* = A_H \tilde{z} = A_H \bar{z}_H = b$ and $c^\transpose z^* = c_H^\transpose \tilde{z}=c_H^\transpose \bar{z}_H=c^\transpose \bar{z}$.
By~\eqref{eqDefnH} and~\eqref{eqExtRaySupp}, we arrive at the final result:
\begin{align*}
 \| z^*  -x^* \|_1 =\| \tilde{z} -x^*_H \|_1
&\le {\sum_{i\in I}} (\lambda_i - \lfloor \lambda_i \rfloor) \|u^{i}\|_1 \\
&< {|H|} \cdot  (m+1)\cdot \|u^i\|_{\infty} \\
&\leq (m+1)\cdot (m+S)\cdot \Delta.\tag*{$\qed$}
\end{align*}
\end{proof}

\begin{proof}[of Theorem~\ref{DeltaSpars}]
Let $z^*$ be an optimal solution of~\eqref{IP} with minimum support.
The definition of $S$ states that ${S} := |\supp (z^* )|$.
Define $\tilde{A}\in\mathbb{Z}^{m\times {S}}$ as the submatrix of $A$ corresponding to the support of $z^*$.
If ${S}\leq 2m$, then the result holds.
Thus, assume that ${S}> 2m$ which implies $\log( \sfrac{{S}}{m})<(\sfrac{{S}}{m})-1$.
Theorem 1 in Aliev et al.~\cite{ADEOW2018} states that
\[
{S} < m+\log \left(\sqrt{\det (\tilde{A}{\tilde{A}}\strut^{\transpose})}\right).
\]
The Cauchy-Binet formula for $\det (\tilde{A}\tilde{A}\strut^\transpose)$ states that
\[
\det(\tilde{A} \tilde{A}\strut^\transpose) = \sum_{\substack{B \text{ is an } m \times m \\\text{submatrix of } \tilde{A}}} \det(B)^2.
\]
See, e.g.,~\cite{HJ2012}.
Combining the previous inequalities yields
\begin{align*}
{S} < m+\log \left(\sqrt{\det (\tilde{A}\tilde{A}\strut^\transpose)}\right)&  \leq m+\log \left(\sqrt{\binom{{S}}{m}\Delta^2}\right)\\[.1 cm]
&\leq m+\log \left({S}^{m/2}\Delta \right)\\
&=m+\frac{m}{2}\log\left( \frac{{S}}{m}\right)+\frac{m}{2}\log(m) +\log (\Delta) \\&
< m+\frac{m}{2}\left(\frac{{S}}{m}-1\right)+\frac{m}{2}\log (m) +\log (\Delta) \\&
=\frac{{S}}{2}+\frac{m}{2}+\frac{m}{2}\log (m) +\log (\Delta).
\end{align*}
Therefore,
\[
|\supp(z^*)| = {S}<m+m\log (m) +2\log (\Delta) \leq 2m\log \bigl(\sqrt{2m} \cdot \Delta^{1/m}\bigr).\tag*{$\qed$}
\]

\end{proof}

\begin{proof}[of Corollary \ref{DeltaSparsMIP}]
  Let $z^*$ be {an optimal \eqref{MIP} solution} with minimal support.
  %
  By applying Theorem \ref{DeltaSpars} to the standard form integer program with constraint matrix $A_{\mathcal{I}}$ and right hand side $b-A_{\mathcal{J}}z^*_{\mathcal{J}}{\in\mathbb{Z}^m}$, where $\mathcal{J}:=\{1,\dots,n\}\setminus \mathcal{I}$, we see that
  %
  \[
  |\supp (z^*_{\mathcal{I}} )|< 2m\log \bigl(\sqrt{2m}\cdot \Delta^{1/m}\bigr).
  \]
  %
    Similarly, by considering the standard form linear program with constraint matrix $A_{\mathcal{J}}$ and right hand side $b-A_{\mathcal{I}}z^*_{\mathcal{I}}$, we see that
  %
  \(
|\supp(z^*_{\mathcal{J}})|\le m.
  \)
  %
  Hence,
  %
  \[
  |\supp(z^*)| \le  |\supp(z^*_{\mathcal{J}})| + |\supp(z^*_{\mathcal{I}})|   \le m + 2m\log \bigl(\sqrt{2m}\cdot \Delta^{1/m}\bigr).\tag*{$\qed$}
  \]
  %
\end{proof}

\section{Results on proximity}\label{sec:proximity}

\begin{proof}[of Theorem \ref{DeltaProx}]
For now, assume that $m \ge 2$.
Combining Lemma \ref{MixedProx} with Theorem~\ref{DeltaSpars} demonstrates that there exists an optimal \eqref{IP} solution $z^*$ satisfying
\[
\begin{split}
\|z^* -x^*\|_1 &<(m+1)\cdot (m+S)\cdot \Delta \\
&\leq (m+1) \cdot 2m\log (2\sqrt{m}\cdot \Delta^{1/m})\cdot\Delta\\
&\leq 3m^2 \log (2\sqrt{m}\cdot \Delta^{1/m})\cdot\Delta.
\end{split}
\]
This completes the proof when $m \ge 2$.

It is left to consider the case $m  = 1$.
Here we have $\Delta = \|A\|_{\infty}$.
The proximity bound~\eqref{eqEWEntryBound} states that there exists an optimal solution $z^*$ to~\eqref{IP} satisfying
\[
\|z^* - x^*\|_1 \le 2 \cdot \|A\|_{\infty}+1 = 2\Delta+1 < 3\Delta \le 3m^2 \log (2\sqrt{m}\cdot\Delta^{1/m})\cdot \Delta .
\]
This completes the proof.
\qed
\end{proof}

We use the following result to prove Theorem~\ref{eqThmEntry}.
\begin{lem}[Theorem 1 in~\cite{SumSubdet}]\label{lemAppx}
For every $\epsilon > 0$, there exists an $m \times m$ submatrix $B$ of $A$ satisfying
\[
\Delta \le |\det(B)| \cdot (e \cdot \ln\left((1+\epsilon) \cdot m)\right)^{m/2}.
\]
The matrix $B$ can be found in time that is polynomial in $m,n$, and $1/\epsilon$.
\end{lem}
Notice that selecting $\epsilon = 1/m$ in Lemma~\ref{lemAppx} yields the approximation factor
\begin{align*}
\Delta & \le |\det(B)| \cdot \left(e \cdot \ln\left(m+1\right)\right)^{m/2} \\
& = |\det(B)| \cdot  \left(\frac{e}{\log(e)} \cdot \log(m+1)\right)^{m/2}\\
& \le |\det(B)| \cdot (2 \cdot \log(m+1))^{m/2},
\end{align*}
which is precisely~\eqref{eqDetApprox}.

\begin{proof}[of Theorem~\ref{eqThmEntry}]
Let $B$ be an $m\times m$ submatrix of $A$ satisfying~\eqref{eqDetApprox}.
There exists a unimodular matrix $U \in \mathbb{Z}^{m\times m}$ such that $UB$ is an upper triangular matrix with non-negative diagonal entries $d_i$.
The so-called row-style Hermite normal form is a transformation satisfying these properties, and the corresponding unimodular matrix $U$ can be computed in polynomial time, see~\cite{AS1986}.

Unimodular matrices preserve the absolute value of $m\times m$ determinants, so $|\det(B)| = |\det(UB)|$.
By~\eqref{eqDetApprox} we see that
\[
\begin{array}{rl}
\displaystyle \Delta \le |\det(B)| \cdot  (2 \cdot \log(m+1))^{m/2} & =\displaystyle   |\det(UB)| \cdot  (2 \cdot \log(m+1))^{m/2}\\[.25 cm]
&\displaystyle = \bigg(\prod_{i=1}^m d_i \bigg)\cdot  (2 \cdot \log(m+1))^{m/2} \\ [.5 cm]
&\displaystyle \le \|UB\|_{\infty}^m \cdot  (2 \cdot \log(m+1))^{m/2}.
\end{array}
\]

Therefore, we may apply Theorem~\ref{DeltaProx} to obtain the bound
\begin{align*}
\|z^* -x^*\|_1  < &3m^2 \log (2\sqrt{m}\cdot \Delta^{1/m}) \cdot \Delta\\
 < & 3m^2  \log (2\sqrt{2m\log (m+1)} \|UB\|_\infty  ) \cdot (2\log (m+1))^{m/2} \cdot\|UB\|_\infty ^m.
\end{align*}
This completes the proof.
\qed
\end{proof}

Next, we present a proof of Corollary \ref{corProxPlusSparsity}.
We advise the reader that the proof is similar to the proof of Lemma~\ref{MixedProx}.

\begin{proof}[of \rm{Corollary \ref{corProxPlusSparsity}}]
Let $z^*$ be an optimal solution to \eqref{GIP} with minimal support on the first $n$ components.
Consider the $n$-dimensional integer program obtained by fixing the last $d$ variables of \eqref{GIP} to the last $d$ components of $z^*$.
Similarly, consider the $n$-dimensional linear program obtained by fixing the last $d$ variables of (GLP) to the last $d$ components of $x^*$.
These lower dimensional problems are in standard form.
Therefore, by applying Theorem \ref{DeltaSpars} to these lower dimensional problems and recalling $\Delta_m(A) \le \delta$, we see that
\[
\bar{S}:=|\supp (x^* ) \cup \supp (z^* )|\leq \min \bigl\{ n,m+2m\log (\sqrt{2m}\cdot\delta^{1/m}) \bigr\} +d .
\]
The conclusion of Corollary \ref{corProxPlusSparsity} follows directly from the inequality
\[
\|z^*-x^*\|_1 <\min\{m+t+1,n+d\} \cdot \bar{S} \cdot \delta,
\]
and we complete the proof of the corollary by demonstrating that the latter inequality holds.
For this, we project the original optimization problems onto the union of the supports of $x^*$ and $z^*$.
To simplify the presentation, we assume that $\bar{S}=n+d$.
The other case is similar.

As in the proof of Lemma~\ref{MixedProx}, we create a pointed cone from the constraints defining~\eqref{GIP}.
In order to assure a pointed cone, we introduce redundant constraints.
Let $b_3 \in \mathbb{Z}^d$ be the vector where every component is $\lceil \|x^*\|_\infty \rceil+ \|z^*\|_\infty$, and define
\[
D :=
\begin{pmatrix}
 0 & C \\-I_n & 0 \\ 0 & I_d
 \end{pmatrix}\in\mathbb{Z}^{(t+n+d)\times (n+d )} \quad \text{and} \quad
 f=\begin{pmatrix}
 b_2 \\ 0 \\ b_3
 \end{pmatrix}\in\mathbb{Z}^{t+n+d}.
\]
By construction, $z^*$ is an optimal solution to the integer program
 %
 \[
 \max\left\{ c^\transpose z  : [A,B] z = b_1, ~Dz \leq f,~z \in\mathbb{Z}^{n+d} \right\},
 \]
 %
and $x^*$ is an optimal vertex solution to the corresponding linear relaxation.
 %

 Subdivide the rows of $D$ such that $D_1 z^* < D_1 x^* $ and $D_2 z^* \geq D_2 x^*$.
 %
 Define the polyhedral cone

 %
 %
 \[
 K :=\left\{ u\in\mathbb{R}^{n+d } : [A,B]u=0,~\begin{pmatrix} D_1 \\ - {D}_2 \end{pmatrix} u \le 0\right\}.
 \]
 %
 Observe that $z^*-x^*\in K$.
 %
 Moreover, the introduction of $b_3$ and $I_d$ ensures that $\rank (D)=n+d$ and that $K$ is pointed.

 Let $U$ be a finite set generating the extreme rays of $K$.
 %
The proof of Claim~\ref{claimExtRays} can be used to demonstrate that for each $\tilde{u} \in U$ we have
 %
 \[
 |\supp(\tilde{u})|\le \min\{m+t+1,n+d\},
 \]
 %
 and each $\tilde{u} \in U$ can be scaled such that $\tilde{u}\in\mathbb{Z}^{n+d}$ and $\|\tilde{u}\|_{\infty}\le \delta$.
 %
The main difference that arises when repeating this proof is that the matrices $D_1$ and $D_2$ contain rows of $[0, C]$ rather than simply rows from the identity matrix as was the case in the proof of Lemma~\ref{MixedProx}.
It is this difference that necessitates the choice of the data parameter $\delta$ and dictates its definition.

 %
 %
 %

By Carath\'eodory's theorem, there exist $k \le \bar{S}$ vectors $u^{1},\dots ,u^{k} \in U$ and coefficients $\lambda_1 ,\dots ,\lambda_k \in \mathbb{R}_{\ge 0}$ such that
 %
 $
 z^* -x^*=\sum_{i=1}^k \lambda_i u^{i} .
 $
 %
 Because $z^* -\sum_{i=1}^k \lfloor\lambda_i \rfloor u^{i}$ is also an optimal solution to \eqref{GIP}, we can assume, without loss of generality, that $\lambda_1, \dotsc, \lambda_k < 1$ (the reasoning is similar to that in the proof of Lemma~\ref{MixedProx}).
 This implies that
 %
 \begin{equation*}
 \| z^* -x^* \|_1 \le \sum_{i=1}^k \lambda_i \|u^{i}\|_1 <\min \{ m+t+1,n+d \}\cdot \bar{S}\cdot \delta.\tag*{$\qed$}
 \end{equation*}
 %
 \end{proof}

\noindent\textbf{Acknowledgements.} J. Lee was supported in part by ONR grant N00014-17-1-2296.

\bibliographystyle{splncs04}

redpajama_set_name: RedPajamaArXiv


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My lab days at Tome have a long history of weird audio projects, including a few Shepard Tone generators and a tool to plot the mandelbrot set in a field of sound (It sounded Okay). In May of this year, I went to Moogfest in Durham, North Carolina. There was a group of researchers there from Virginia Tech with a large speaker array called the Cube, an array of over 150 speakers arranged in a cube-shaped, four-story building. A few people at The Cube helped me to get a basic view of the current technology used in HDLAs, including Reaper, Max, and various Ambisonics toolkits. You can find some interesting technical information on the cube here.
My idea was essentially just to create a virtual sphere within which sounds can be moved and manipulated. I chose to use Unity and Google Cardboard for this project. They were both perfect for the idea because they are simple and easy, and prototyping is time-consuming. I would have loved to develop this on an Oculus Rift or HTC Vive, but those would have taken far too much time for something that I didn't even really expect to work this well.
This was the least code I've ever written on a lab day. Setting it up couldn't have been simpler. I used a Cardboard demo, the one where there is a cube in front of you and you can pick it up and drag it. I also used 8 separate audio tracks, from a dinky little song I wrote a few days prior.
Make as many copies of the cube as you have tracks and put them wherever you want them to start in the player's field of hearing. Note that sounds that don't start immediately need to be exported with empty space at the beginning so that you don't have to set the timing of tracks in Unity.
The whole thing worked better than I expected. In fact, it feels so natural that some effects aren't obvious at first. I realized this once I tested on my computer instead of on my phone: Moving the 'view' without actually moving your head makes the ambisonic effects much more obvious.


* Ingame personal messages, ingame alliance pages, ingame alliance applications and ingame circular messages.
* Take into account that a member of the game support team might block you on a temporary or permanent basis. This includes both, accounts which might or might not have broken any of the points above.
* At the same time take into consideration that your behavior on any of our services might end up in a permanent or temporary ban from the whole community and its services.
* The Terms and Conditions stand above the rules, please read them as well.
This rule and rule XII - Content go hand in hand. Watch what you say and don't offend people. Remember, those are real people behind those accounts.


We're not just about Cosmetic Dentistry procedures. At Black Swan Dental Spa we provide the highest level of dental care for all the family including consultations, regular health checks & x-rays and routine dental care such as fillings.
We understand how some people feel about visiting the dentist and we are keen to turn each visit into a positive encounter. We want to make coming to see us an enjoyable experience where you leave feeling listened to, privileged, pampered and part of something special – and excited about your next visit! All our prospective clients are invited to a complimentary consultation where they can visit the practice and meet the staff. In a non-clinical environment they can discuss their dental issues and concerns and find out about the most appropriate treatments that are available.
During your regular health review we will listen to your concerns, after which a full oral health assessment will be carried out. This is where the teeth, the gums and an oral cancer screen is done as standard. Digital X-rays will be taken and all issues will be discussed. We also give you a virtual tour of your mouth, using the latest in intraoral camera technology, highlighting any issues that may arise. Any required intervention is then discussed and a Treatment plan will be formulated with a full breakdown of costs.
Also known as composites, filling materials have come of age over these past few years. They are aesthetically pleasing and the latest layering techniques allow the restoration to mimic the layers that occur naturally in our own teeth. Latest technology now allows the filling to be indiscernible from your original tooth, with virtually seamless finishing.
Due to the advancements of durability and strength they now have, they are considered a real alternative to other unsightly fillings. This results in a filling that is as durable as conventional amalgam fillings but with the added advantage of improved appearance.
Root Canal Treatment (RCT) is required when the blood or nerve supply to the tooth has been affected by trauma, infection or decay. This may or may not be accompanied by symptoms of pain.
Inside each tooth is the pulp, which provides the nutrients (in the blood supply) and nerves to the tooth. It appears like a thread running through the tooth. Depending on the tooth anatomy will dictate the number of roots the tooth has and therefore the number of canals present. When the pulp becomes diseased or infected due to various events, it dies. At this stage the pulp will then be removed, the canals cleaned and the tooth sealed. The tooth may then be crowned in order to protect it, depending on the amount of tooth structure that is remaining.