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# Assumptions regarding bootstrap estimates of uncertainty

I appreciate the usefulness of the bootstrap in obtaining uncertainty estimates, but one thing that's always bothered me about it is that the distribution corresponding to those estimates is the distribution defined by the sample. In general, it seems like a bad idea to believe that our sample frequencies look exactly like the underlying distribution, so why is it sound/acceptable to derive uncertainty estimates based on a distribution where the sample frequencies define the underlying distribution?

On the other hand, this may be no worse (possibly better) than other distributional assumptions we typically make, but I'd still like to understand the justification a bit better.

• There are several related questions you might want to look through. Some are listed on the side margin of this page. Here is one regarding when the bootstrap fails and what it means for it to fail. – cardinal May 24 '11 at 21:57

There are several ways that one can conceivably apply the bootstrap. The two most basic approaches are what are deemed the "nonparametric" and "parametric" bootstrap. The second one assumes that the model you're using is (essentially) correct.

Let's focus on the first one. We'll assume that you have a random sample $X_1, X_2, \ldots, X_n$ distributed according the the distribution function $F$. (Assuming otherwise requires modified approaches.) Let $\hat{F}_n(x) = n^{-1} \sum_{i=1}^n \mathbf{1}(X_i \leq x)$ be the empirical cumulative distribution function. Much of the motivation for the bootstrap comes from a couple of facts.

Dvoretzky–Kiefer–Wolfowitz inequality

$$\renewcommand{\Pr}{\mathbb{P}} \Pr\big( \textstyle\sup_{x \in \mathbb{R}} \,|\hat{F}_n(x) - F(x)| > \varepsilon \big) \leq 2 e^{-2n \varepsilon^2} \> .$$

What this shows is that the empirical distribution function converges uniformly to the true distribution function exponentially fast in probability. Indeed, this inequality coupled with the Borel–Cantelli lemma shows immediately that $\sup_{x \in \mathbb{R}} \,|\hat{F}_n(x) - F(x)| \to 0$ almost surely.

There are no additional conditions on the form of $F$ in order to guarantee this convergence.

Heuristically, then, if we are interested in some functional $T(F)$ of the distribution function that is smooth, then we expect $T(\hat{F}_n)$ to be close to $T(F)$.

(Pointwise) Unbiasedness of $\hat{F}_n(x)$

By simple linearity of expectation and the definition of $\hat{F}_n(x)$, for each $x \in \mathbb{R}$,

$$\newcommand{\e}{\mathbb{E}} \e_F \hat{F}_n(x) = F(x) \>.$$

Suppose we are interested in the mean $\mu = T(F)$. Then the unbiasedness of the empirical measure extends to the unbiasedness of linear functionals of the empirical measure. So, $$\e_F T(\hat{F}_n) = \e_F \bar{X}_n = \mu = T(F) \> .$$

So $T(\hat{F}_n)$ is correct on average and since $\hat{F_n}$ is rapidly approaching $F$, then (heuristically), $T(\hat{F}_n)$ rapidly approaches $T(F)$.

To construct a confidence interval (which is, essentially, what the bootstrap is all about), we can use the central limit theorem, the consistency of empirical quantiles and the delta method as tools to move from simple linear functionals to more complicated statistics of interest.

Good references are

1. B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Stat., vol. 7, no. 1, 1–26.
2. B. Efron and R. Tibshirani, An Introduction to the Bootstrap, Chapman–Hall, 1994.
3. G. A. Young and R. L. Smith, Essentials of Statistical Inference, Cambridge University Press, 2005, Chapter 11.
4. A. W. van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998, Chapter 23.
5. P. Bickel and D. Freedman, Some asymptotic theory for the bootstrap. Ann. Stat., vol. 9, no. 6 (1981), 1196–1217.
• Very nice, @cardinal (+1). – user1108 May 26 '11 at 1:59
• Clear explanation, references is given, excellent answer. – vesszabo Jun 23 '18 at 7:35

Here is a different approach to thinking about it:

Start with the theory where we know the true distribution, we can discover properties of sample statistics by simulating from the true distribution. This is how Gosset developed the t-distribution and t-test, by sampling from known normals and computing the statistic. This is actually a form of the parametric bootstrap. Note that we are simulating to discover the behavior of the statistics (sometimes relative to the parameters).

Now, what if we do not know the population distribution, we have an estimate of the distribution in the empirical distribution and we can sample from that. By sampling from the empirical distribution (which is known) we can see the relationship between the bootstrap samples and the empirical distribution (the population for the bootstrap sample). Now we infer that the relationship from bootstrap samples to empirical distribution is the same as from the sample to the unknown population. Of course how well this relationship translates will depend on how representative the sample is of the population.

Remember that we are not using the means of the bootstrap samples to estimate the population mean, we use the sample mean for that (or whatever the statistic of interest is). But we are using the bootstrap samples to estimate properties (spread, bias) of the sampling proccess. And using sampling from a know population (that we hope is representative of the population of interest) to learn the effects of sampling makes sense and is much less circular.

The main trick (and sting) of bootstrapping is that it is an asymptotic theory: if you have an infinite sample to start with, the empirical distribution is going to be so close to the actual distribution that the difference is negligible.

Unfortunately, bootstrapping is often applied in small sample sizes. The common feel is that bootstrapping has shown itself to work in some very non-asymptotic situations, but be careful nonetheless. If your samplesize is too small, you are in fact working conditionally on your sample being a 'good representation' of the true distribution, which leads very easily to reasoning in circles :-)

• that's kind of what I thought, but there's something circular about this reasoning. I'm not a statistician, but my sense was that statistical inference works when your estimators converge rapidly, so even if your sample hasn't converged on the distribution, your inferences are sound. In this case, we're relying on the entire empricial distribution to converge to the actual distribution. Maybe there are theorems saying that some bootstrap estimates converge quickly, but I generally see bootstrapping applied without appealing to such theorems. – user4733 May 24 '11 at 21:15
• The apparent circular reasoning is why it was nicknamed the bootstrap. It felt like people were trying to lift themselves by their own bootstraps. Later Efron showed that it really did work. – Greg Snow May 24 '11 at 22:39
• If the sample size is really small, you need a lot of trust whatever methods yuo use ... – kjetil b halvorsen Apr 19 '18 at 22:22

I would argue not from the perspective of "asymptotically, the empirical distribution will be close to the actual distribution" (which, of course, is very true), but from a "long run perspective". In other words, in any particular case, the empirical distribution derived by bootstrapping will be off (sometimes shifted too far this way, sometimes shifted too far that way, sometimes too skewed this way, sometimes too skewed that way), but on average it will be a good approximation to the actual distribution. Similarly, your uncertainty estimates derived from the bootstrap distribution will be off in any particular case, but again, on average, they will be (approximately) right.


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# Uniform rejection sampling by shifting or rotating bits from CSPRNG output, safe?

Given a CSPRNG (arc4random, using ChaCha20 keystream), one want to use rejection sampling to get random number on a smaller range avoiding modulo bias (arc4random_uniform()).

OpenBSD's arc4random_uniform() implementation draws a 32bits value and tests its fitness, rejecting values that don't fit.

It's not the only possible implementation. In Efficiently Generating a Number in a Range, M.E. O'Neill provides various other ways to generate random number within a range while avoiding the modulo bias.

In particular, there's this so called Bitmask with Rejection (Unbiased) — Apple's Method. Following the link to the actual Apple's implementation, one can see it has another trick:

/*
* Calculate a uniformly distributed random number less than upper_bound
* avoiding "modulo bias".
*
* Uniformity is achieved by trying successive ranges of bits from the random
* value, each large enough to hold the desired upper bound, until a range
* holding a value less than the bound is found.
*/
uint32_t
arc4random_uniform(uint32_t upper_bound)
{
if (upper_bound < 2)
return 0;

// find smallest 2**n -1 >= upper_bound
int zeros = __builtin_clz(upper_bound);
int bits = CHAR_BIT * sizeof(uint32_t) - zeros;
uint32_t mask = 0xFFFFFFFFU >> zeros;

do {
uint32_t value = arc4random();

// If low 2**n-1 bits satisfy the requested condition, return result
uint32_t result = value & mask;
if (result < upper_bound) {
return result;
}

// otherwise consume remaining bits of randomness looking for a satisfactory result.
int bits_left = zeros;
while (bits_left >= bits) {
value >>= bits;
if (result < upper_bound) {
return result;
}
bits_left -= bits;
}
} while (1);
}

Instead of drawing a new value if the current one doesn't fit the range, the value is shifted to discard any bits involved in the fit test, until the value fits or there's not enough unused bit left.

This is especially useful if the CSPRNG is costly, for example, if it requires a system call to generate one value, reducing the amount of time it's invoked, while algorithmically complex, might improve arc4random_uniform() overall speed.

And now my question: given a 32bits value generated by a CSPRNG, given the CSPRNG output is indiscernible from a random stream, that every value is as likely as any other, why discarding every tested bits ?

1. Is it possible to shift the value by one bit at a time and test the resulting value against the range ?
    do {
uint32_t value = arc4random();

for (int bits_left = 32; bits_left >= bits ; bits_left--) {

uint32_t result = value & mask;

if (result < upper_bound) {
return result;

value = value >> 1; // shift right by one bit
}
} while (1);

1. Is it possible to rotate the value by one bit at a time and test the resulting value against the range ?
    do {
uint32_t value = arc4random();

for (int i = 0; i < 32; i++) {

uint32_t result = value & mask;

if (result < upper_bound) {
return result;

value = ror32(value, 1); // rotate right by one bit
}
} while (1);

Are those optimization safe to build arc4random_uniform ?

If not, on what basis ?

Are those optimization safe to build arc4random_uniform ?

No, they are not.

If not, on what basis ?

Because, after we test the value of result and reject it (that is, it is >= upper_bound, the bits in the tested region are not uniform; we know that those bits within value are also >= upper_bound (and so values less than that will never appear). As those bits are nonuniform, reusing them in future tests will give nonuniform results.

Let us give a simple example: suppose upper_bound = 3 (and hence mask = 3). Then, on the first iteration, if the lower two bits of value are 0, 1 or 2, we'll return that with equal probability, not an issue. However, if the lower two bits happen to be 3 (that is, the bits are 11), we won't return that iteration, and so we'll go to the next. Your ideas would shift the value right one bit, resulting in the lower two bits being x1 (where 'x' is the original bit 2 which we haven't tested yet), that is, the lower two bits will be either the value 1 or the value 3. If it's 1, that iteration will return that; otherwise it'll skip to the next iteration. In no case will the second iteration return 0 or 2 (and similarly in latter iterations); hence we have a strong bias towards 1.

The original code (which discards all the bits tested after a rejection) doesn't have this problem.

• Thanks for the explanation ! It would also be the same issue with a rotation to the left instead of right ! Aug 2 at 11:53
• Yes. Very basically, unless you have an exact 50% chance of the bit being one or zero then you'd run into problems. Of course, if it had a chance of 50% then you would not have to reject it in the first place. So if it doesn't fit in your model then you have to reject it, or compensate for the bias (which is tricky). Note that if you do these tests bit by bit then on average you have an overhead of about 1.7 bit... You can try and optimize it further, but why? Aug 2 at 12:02
• @poncho could you get away with shifting by popcnt(n)? Think its only the 1 bits in upper_bound that cause the issue as they can end up fixing certain lower bits. But shifting up by popcnt(n) will always shift out as many bits as where potentially forcing trailing 1s. I.e if you have upper_bound = 6 for value & mask >= n must be 1 in position 2/3 which are shifted out, but lower bit can be anything.
– Noah
Aug 2 at 13:04
• @Noah: I assume you mean popcnt(result); you have to be careful, you know that result is a value between upper_bound and mask, but could be any value in that range. For example, if upper_bound = 5, then result is one of 5, 6, 7 - that is, the lsbit is also biased toward 1. Now, there are algorithms that do harvest that amount of entropy to try to rely on fewer bits from the rng; however those algorithms are not cheap. I'm sure Apple knew about those fancier algorithms, but they don't save that much in most cases, and so Apple went with the overall cheaper algorithm. Aug 2 at 13:28
• @poncho err popcnt(upper_bound) (although that is wrong), really its clz(upper_bound) - ctz(upper_bound) + using rol. The lower 0s in upper_bound are entirely unrelated to the comparison so there is no bias in keeping them around.
– Noah
Aug 3 at 4:47

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2019 CMS Summer Meeting

Regina, June 7 - 10, 2019

# Schedule - by Session

Detailed session schedules will be posted on the web site beginning in late April. Once the schedules are made available to us by the organizers, we will post them as quickly as possible. Please note that schedules are subject to change without notice. All scientific sessions will be held at the University of Regina.

 Assessment in Mathematics Org: Shannon Ezzat (Winnipeg) and Rebecca McKay (UNB) Sunday June 9  (ED 623, Education Building) 8:00 - 8:30 Darja Barr (University of Manitoba), Taking Math Students from 'Blah' to 'Aha': How Can Assessment Help? 8:30 - 9:00 Rebecca Milley (Grenfell Campus, Memorial University), Reading, Writing, Arithmetic: Assessment Strategies for Readings and Written Work in Mathematics 9:00 - 9:30 Lauren DeDieu (University of Calgary), Using Assessments to Boost Motivation in a Second-Year Linear Algebra Class 9:30 - 10:00 Christopher Eagle (University of Victoria), In-class formative assessment in proof-heavy courses 10:00 - 10:30 Rebecca McKay (University of New Brunswick, Saint John), Active Assessment 16:00 - 16:30 Discussion Session 16:30 - 17:00 Danny Dyer (Memorial University of Newfoundland) 17:00 - 17:30 Patrick Reynolds (University of New Brunswick), Assessing and Grading with Crowdmark 17:30 - 18:00 Marie Langlois (Cornell University), Using Free Online Software to Efficiently Assess Students Categorical Approaches to Topology and Geometry Org: Marzieh Bayeh (Dalhousie), Darien DeWolf (St Francis Xavier) and Dorette Pronk (Dalhousie) Saturday June 8 16:30 - 17:00 Jonathan Scott (Cleveland State University), Wasserstein distance for generalized persistence modules and abelian categories, ED 314, Education Building 17:30 - 18:00 Seth Wolbert (University of Manitoba), Fibrations as presentations of actions on stacks, ED 314, Education Building Sunday June 9 8:00 - 8:30 Robin Cockett (University of Calgary), Hyperconnections, ED 314, Education Building 8:30 - 9:00 Chris Kapulkin (Western University), Cubical models of higher category theory, ED 314, Education Building 9:00 - 9:30 Zach Lindsey (Western University), Cubical models of higher category theory, ED 314, Education Building 9:30 - 10:00 Hellen Colman (Wilbur Wright College), Equivariant motion planning, ED 314, Education Building 10:00 - 10:30 Rory Lucyshyn-Wright (Brandon University), Functional distribution monads and $\tau$-additive measures 16:00 - 16:30 Laura Scull (Fort Lewis College), Defining Bicategories of Fractions with Small Hom Sets, ED 314, Education Building 16:30 - 17:00 Dorette Pronk (Dalhousie University), Nice properties of the bicategory of orbigroupoids, ED 314, Education Building 17:00 - 17:30 Jordan Watts (Central Michigan University), Bredon Cohomology for Transitive Groupoids, ED 314, Education Building 17:30 - 18:00 Joel Villatoro (KU Leuven), Geometric structures on differentiable stacks, ED 314, Education Building Monday June 10 8:00 - 8:30 Kristine Bauer (University of Calgary), The Kleisli category of a pseudomonad for chain complexes, CK 187, Centre for Kinesiology 8:30 - 9:00 JS Lemay (Oxford University), The Poincaré Lemma for Codifferential Categories with Antiderivatives, CK 187, Centre for Kinesiology 9:00 - 9:30 Ben McAdam (University of Calgary), Involution Algebroids, CK 187, Centre for Kinesiology 9:30 - 10:00 Geoff Cruttwell (Mount Allison University), Curvature and torsion without negatives, CK 187, Centre for Kinesiology 10:00 - 10:30 Marzieh Bayeh (Dalhousie University), Orbit Category and The Category of Orbit Classes, CK 187, Centre for Kinesiology 14:45 - 15:15 Darien Dewolf (St. Francis Xavier University), The equivalence of ordered groupoids and left cancellative categories using double categories, CK 187, Centre for Kinesiology 15:15 - 15:45 Curran McConnell (Dalhousie University), Combinatorics of spaces of trees: an application of topology to phylogenetics, CK 187, Centre for Kinesiology 15:45 - 16:15 Michael Lambert (Dalhousie University), A Site for Continuous 2-Group Actions, CK 187, Centre for Kinesiology 16:15 - 16:45 Jonathan Gallagher (Dalhousie University), Etale Subobject classifiers in SDG and tangent categories, CK 187, Centre for Kinesiology Contributed Papers Org: Allen Herman (Regina), Alexander Litvak (Alberta) and Karen Meagher (Regina) Sunday June 9  (CK 185, Centre for Kinesiology) 16:00 - 16:30 A. Sarobidy Razafimahatratra (University of Regina), Erdős–Ko–Rado Theorem for permutation groups 16:30 - 17:00 Zhenyuan Zhang (University of Waterloo), On discrete-time self-similar processes with stationary increments 17:00 - 17:30 Hossein Pourali (Brandon University), ALGEBRAIC AND GRAPH THEORETIC ASPECTS IN LATTICES AND POSETS 17:30 - 18:00 Saleh Mustafa (University of Regina), Higher Rank Numerical Ranges for Certain Non-normal Matrices Equivariant Methods in Differential and Algebraic Geometry Org: Lisa Jeffrey (Toronto), Liviu Mare (Regina) and Leonardo Mihalcea (Virginia Tech) Saturday June 8  (ED 106.1, Education Building) 8:00 - 8:30 Anders Buch (Rutgers University), Positivity of minuscule quantum K-theory 8:50 - 9:20 Jenna Rajchgot (University of Saskatchewan), Grobner bases for certain type C Kazhdan-Lusztig ideals 9:40 - 10:10 Matthias Franz (University of Western Ontario), The number of connected orbit types in a $G$-manifold 16:00 - 16:30 Alejandro Adem (University of British Columbia), Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy 16:40 - 17:10 Chi-Kwong Fok (University of Auckland), Twisted K-theory and extended Verlinde algebra 17:20 - 17:50 Jeffrey Carlson (University of Toronto), The equivariant K-theory of a cohomogeneity-one action Sunday June 9  (ED 106.1, Education Building) 8:00 - 8:30 Steven Rayan (University of Saskatchewan), Linearizations of character varieties of curves: geometry and mirror symmetry 8:50 - 9:20 Evan Sundbo (University of Saskatchewan), The Geometry of Twisted Cyclic Quiver Varieties 9:40 - 10:10 Jordan Watts (Central Michigan University), Classifying Spaces for Diffeological Groups 16:00 - 16:30 Kirill Zanoulline (University of Ottawa), Localized Landweber-Novikov operations on generalized cohomology 16:40 - 17:10 Changlong Zhong (SUNY Albany), On the K-theoretic stable bases 17:20 - 17:50 Tom Baird (Memorial University of Newfoundland), E-polynomials of character varieties associated to a real curve Monday June 10  (ED 106.1, Education Building) 8:00 - 8:30 Derek Krepski (University of Manitoba), An analogue of Kostant’s formula for Lie group-valued moment maps 8:50 - 9:20 Yiannis Loizides (Penn State University), Quasi-polynomials, asymptotics and [Q,R]=0 9:40 - 10:10 Mark Hamilton (Mount Allison University), Integral integral affine geometry, quantization, and Riemann-Roch. 14:45 - 15:15 Jeremy Lane (University of Geneva), Volume exhausting, $T$-equivariant symplectic embeddings of toric manifolds into regular coadjoint orbits 15:25 - 15:55 Peter Crooks (Northeastern University), Kostant-Toda lattices and invariant theory 16:05 - 16:35 Rebecca Goldin (George Mason University), Schubert Calculus, Schubert Operators, and Positivity Finite and Infinite Dimensional Structures in Non-Commutative Analysis Org: Martin Argerami and Remus Floricel (Regina) Saturday June 8  (ED 191, Education Building) 8:00 - 8:30 Dilian Yang (University of Windsor), KMS states of self-similar k-graph C*-algebras 8:30 - 9:00 Matthias Neufang (Carleton University), Solution to several problems regarding tensor products and crossed products of $C^*$- and von Neumann algebras 9:00 - 9:30 Marcelo Laca (University of Victoria), Reconstructing directed graphs 9:30 - 10:00 Jason Crann (Carleton University), An equivariant weak expectation property and amenable actions 10:00 - 10:30 Paul Skoufranis (York University), Majorization, Convexity, and Expectations 16:00 - 16:30 Nico Spronk (University of Waterloo), Fixed points of contractive measures acting by convolution 16:30 - 17:00 Masoud Khalkhali (Western University), Von Neumann information entropy, second quantization, and spectral action 17:00 - 17:30 Volker Runde (University of Alberta), Amenability of the Fourier algebra in the completely bounded multiplier norm 17:30 - 18:00 Daniel Drimbe (University of Regina), Prime II$_1$ factors arising from actions of product groups Sunday June 9  (ED 191, Education Building) 8:00 - 8:30 Vern Paulsen (University of Waterloo), Preservation of the joint essential matricial range 8:30 - 9:00 Heath Emerson (University of Victoria), Transversals and Connes' duality for the irrational rotation algebra 9:00 - 9:30 Francesco Fidaleo (University of Rome Tor Vergata), Uniquely Ergodic $C^*$-Dynamical Systems for the noncommutative 2-torus 9:30 - 10:00 Raphael Clouatre (University of Manitoba), Residual finite-dimensionality for general operator algebras 10:00 - 10:30 Berndt Brenken (University of Calgary), Partial isometries implementing cpc C*- dynamical systems 16:00 - 16:30 Jiun-Chau Wang (University of Saskatchewan), Probability measures in bi-free probability 16:30 - 17:00 Cristian Ivanescu (MacEwan University), Pedersen ideals of tensor products of nonunital C*-algebras 17:00 - 17:30 Edward Timko (University of Manitoba), The Spectrum of Constrained Model $d$-tuples 17:30 - 18:00 Anamaria Savu (University of Alberta), Conservative Restricted Solid-on-Solid Model Finite Geometry Org: Tim Alderson (UNB) and Brett Stevens (Carleton) Saturday June 8  (CK 185, Centre for Kinesiology) 9:00 - 9:30 Tim Alderson (University of New Brunswick Saint John), $t$-Extensions of Linear Codes 9:30 - 10:00 James McQuillan (Western Illinois University), Desargues configurations with self-conjugate points 10:00 - 10:30 Aiden Bruen (Carleton University), An extension of Desargues Theorem 16:00 - 16:30 Brett Stevens (Carleton University), Affine planes with ovals for blocks 16:30 - 17:00 John Sheekey (University College Dublin), Finite Geometry and Rank-Metric Codes 17:30 - 18:00 David Wehlau (Royal Military College of Canada), Planes, Division Sequences and ZZ-topes Functional and Complex Analysis Org: Douglas Farenick (Regina) and Javad Mashreghi (Laval) Saturday June 8  (ED 315, Education Building) 8:00 - 8:30 Damir Kinzebulatov (Université Laval), A new look at the KLMN theorem 8:30 - 9:00 Mohammad Shirazi (University of Manitoba), Grunsky and Faber Operators for Riemann Surfaces with One Border 9:00 - 9:30 Christopher Ramsey (Grant MacEwan University), What is and is not a Tensor algebra 9:30 - 10:00 Ryan Tessier (University of Regina), Purity of the Identity Map on the Operator System generated by the Free Group 10:00 - 10:30 Raphael Clouatre (University of Manitoba), Uniform quotients and $\mathrm{C}^*$-envelopes on the Drury-Arveson space 16:00 - 16:30 Abdel Rahman (University of Regina), Homogeneous Levi Foliations 16:30 - 17:00 Ed Timko (University of Manitoba), Row Contractions Constrained by Higher Order Vanishing Ideals. 17:00 - 17:30 Bruce Gilligan (University of Regina), Pseudoconvex homogeneous manifolds 17:30 - 18:00 Richard Fournier (Dawson College), A Schwarz lemma for locally univalent meromorphic functions 18:00 - 18:30 Javad Mashreghi (Université Laval), Approximation schemes in function spaces High-Dimensional Problems in Finance and Quantitative Research Org: Taehan Bae and Andrei Volodin (Regina) Saturday June 8  (ED 438, Education Building) 8:00 - 8:30 Alexander Melnikov (University of Alberta), On Option Pricing Methods in Modern Mathematical finance 8:30 - 9:00 Xuemiao Hao (University of Manitoba), Sharp Tail Estimate for Aggregate Critical Illness Claims in a Large Population 9:00 - 9:30 Yangho Choi (Hanyang University), Macroscopic Modeling of Data Breach Risk with Spatial and Temporal Autocorrelation 9:30 - 10:00 Shanoja Naik (Registered Nurses Association of Ontario), On Wishart Process and Sovereign Credit Risk Modelling 10:00 - 10:30 Naeima Ashleik (University of Saskatchewan), Learning for Contingency Tables and Survival Data Using Imprecise Probabilities 16:00 - 16:30 Syed Ejaz Ahmed (Brock University), Implicit Bias in Big Data Analytics 16:30 - 17:00 Shakhawat Hossain (University of Winnipeg), Estimation strategy of multilevel model for ordinal longitudinal data 17:00 - 17:30 Thuntida Ngamkham (University of Calgary), Confidence intervals for a ratio of binomial proportions 17:30 - 18:00 Salma Saad (University of Regina), Asymptotic Analysis of Method of Moments Estimators of Parameters p and m for the Binomial Distribution Indigenization and Reconciliation in Mathematics Org: Douglas Farenick (Regina) and Keith Taylor (Dalhousie) Saturday June 8  (ED 558, Education Building) 8:00 - 8:30 Keith Taylor (Dalhousie University), What can the CMS do about reconciliation? 8:30 - 9:00 Brian Forrest (University of Waterloo), Expanding Mathematics Educational Opportunites for Indigenous Teachers 9:00 - 9:30 Veselin Jungic (Simon Fraser University), Changing Lives or Scratching the Surface: Five Years of the SFU Academic Summer Camp for Aboriginal Students 9:30 - 10:00 Darja Barr (University of Manitoba), The Impact of Working Together 10:00 - 10:30 Melania Alvarez (University of British Columbia), Engaging Indigenous communities through math outreach 16:00 - 16:30 Edward Doolittle (First Nations University of Canada) 16:30 - 17:00 Kathy Nolan (University of Regina), A Reframing of Mathematics through Critical and Culturally Responsive Pedagogies 17:00 - 17:30 Gale Russell (University of Regina), Truth before Reconciliation in Mathematics and Mathematics Education: An Invitation to Action 17:30 - 18:00 Open Discussion Sunday June 9  (ED 558, Education Building) 8:30 - 9:00 Arzu Sardarli (First Nations University of Canada), Use of Indigenous elements in teaching introductory Statistics courses 9:00 - 9:30 Doug Farenick (University of Regina), Acts of Reconciliation -- A Scientist's Experience 9:30 - 10:00 Open Discussion 10:00 - 10:30 Open Discussion Mathematical Techniques for Analysing Quantum Structures and Materials Org: Steven Rayan and Artur Sowa (Saskatchewan) Saturday June 8  (ED 106.2, Education building) 8:00 - 8:30 Alex Zagoskin (Loughborough University), Towards the qualitative theory of large quantum coherent structures 8:30 - 9:00 Cihan Okay (University of British Columbia), Topology of quantum contextuality 9:00 - 9:30 Joseph Maciejko (University of Alberta), Strongly interacting topological phases of matter 9:30 - 10:00 Robert Green (University of Saskatchewan), Numerical Many Body Models for Synchrotron Spectroscopy of Quantum Materials 10:00 - 10:30 Ray Spiteri (University of Saskatchewan), Quantum control for high-fidelity multi-qubit gates 16:00 - 16:30 Neil J. Ross (Dalhousie University), Number-Theoretic Methods in Quantum Compiling 16:30 - 17:00 Gilad Gour (University of Calgary), Mathematical structures and features of quantum resource theories 17:00 - 17:30 Artur Sowa (University of Saskatchewan), Qubits, wavelets, fractals, bands Matrix Theory and its Applications Org: Shaun Fallat (Regina) and Shahla Naserasr (Brandon) Sunday June 9  (ED 106.2, Education building) 8:00 - 8:30 Murray R. Bremner (University of Saskatchewan), Computing a short basis for the nullspace of a modular matrix 8:30 - 9:00 Pietro Paparella (University of Washington Bothell), Matricial Proofs of Some Classical Results about Critical Point Location 9:00 - 9:30 Keivan Monfared (University of Victoria), An Analog of Matrix Tree Theorem for Signless Laplacians 9:30 - 10:00 Colin Garnett (Black Hills State University), Non-sparse Companion Matrices 10:00 - 10:30 Xiaohong Zhang (University of Manitoba), Perfect state transfer on weighted paths 16:00 - 16:30 Lon Mitchell (University of South Florida St. Petersburg), Optimal Colin de Verdière Matrices for Complete Multipartite Graphs 16:30 - 17:00 Sivaram K. Narayan (Central Michigan University), Graph Complement Conjecture for Classes of Shadow Graphs 17:00 - 17:30 Harmony Zhan (Université de Montréal), Quantum state transfer in the algebra of the Johnson scheme 17:30 - 18:00 Kerry Tarrant (University of Iowa), The Good, The Bad, and The Ugly: Minimally Cop Win and Maximally Robber Win Graphs Monday June 10  (ED 106.2, Education building) 8:00 - 8:30 Robert Bailey (Memorial University of Newfoundland - Grenfell Campus), Orthogonal matrices with zero diagonal 8:30 - 9:00 Chun-Hua Guo (University of Regina), Explicit convergence region of Newton's method for the matrix $p$th root 9:00 - 9:30 Rajesh Pereira (University of Guelph), The real joint numerical range and the real higher rank numerical range 9:30 - 10:00 Samuel Cole (University of Manitoba), Spectral recovery of stochastic block models on graphs and hypergraphs 10:00 - 10:30 Mahsa Nasrollahi Shirazi (University of Regina), Erdős-Ko-Rado theorem for t-intersecting families of perfect matchings 14:45 - 15:15 Gurmail Singh (University of Regina), Encoding the vertices of a hyper cube 15:15 - 15:45 Eugene Bilokopytov (University of Manitoba), From Principal Minor Assignment problem for matrices to characterization of the isometries on Hilbert Spaces 15:45 - 16:15 Robert Craigen (University of Manitoba) 16:15 - 16:45 Nathan Krislock (Northern Illinois University) Probabilistic Methods in Geometric Functional Analysis and Convexity Org: Grigoris Paouris (Texas A&M), Alina Stancu (Concordia), Beatrice-Helen Vritsiou (Alberta) and Vlad Yaskin (Edmonton) Saturday June 8  (ED 193, Education Building) 8:00 - 8:30 Elisabeth Werner (Case Western Reserve University), Entropy inequalities for log concave functions 8:30 - 9:00 Galyna Livshyts (Georgia Institute of Technology), Smallest singular value of inhomogeneous random square matrices via double counting and random rounding 9:00 - 9:30 Konstantin Tikhomirov (Georgia Institute of Technology), Small ball probability for the condition number of random matrices 9:30 - 10:00 Arnaud Marsiglietti (University of Florida), Hyperplane conjecture and central limit theorem 10:00 - 10:30 Piotr Nayar (University of Warsaw), The log-concave moment problem 16:00 - 16:30 Mokshay Madiman (University of Delaware), Sharp moment-entropy inequalities for log-concave distributions 16:30 - 17:00 Yair Shenfeld (Princeton University), Extremals in Minkowski's quadratic inequality 17:00 - 17:30 Kateryna Tatarko (University of Alberta), On the solution to the reverse isoperimetric problem 17:30 - 18:00 Susanna Dann (Universidad de los Andes), Affine isoperimetric inequalities on flag manifolds. 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(Memorial) and Ryan Tifenbach (Mount Allison) Saturday June 8  (CK 187, Centre for Kinesiology) 8:00 - 8:30 Anthony Bonato (Ryerson), Limited information Cops and Robbers games 8:30 - 9:00 Andrea Burgess (University of New Brunswick St. John), Cops that surround a robber 9:00 - 9:30 Ryan Hayward (University of Alberta), Searching for Winning Strategies in Hex 9:30 - 10:00 Shahin Kamali (University of Manitoba), On the complexity of burning and broadcasting problems 10:00 - 10:30 David Pike (Memorial University of Newfoundland), The Firebreak Problem Recent Advances in Probability and Stochastics Org: Michael Kozdron (University of Regina) and Gregory Lawler (University of Chicago) Saturday June 8  (ED 623, Education Building) 9:00 - 9:30 Christian Benes (Brooklyn College), Rates of Convergence for the Simple Random Walk Green's Function 9:30 - 10:00 Larissa Richards (University of Toronto), The polynomial rate of convergence of critical interfaces. 10:00 - 10:30 Arno Berger (University of Alberta), Best Kantorovich and Levy approximations on the real line 16:00 - 16:30 Yinon Spinka (University of British Columbia), A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$ 16:30 - 17:00 Kasun Fernando Akurugodage (University of Toronto), Higher order asymptotics for Large Deviations 17:00 - 17:30 Sarai Hernandez Torres (University of British Columbia), Scaling limits of uniform spanning trees in three dimensions Representation Theory of Groups Defined Over Local Fields Org: Monica Nevins (Ottawa) and Jerrod Smith (Calgary) Saturday June 8  (ED 312, Education Building) 8:00 - 8:30 Paul Mezo (Carleton University), Equivalent definitions of Arthur-packets for real classical groups 8:30 - 9:00 Nicolas Arancibia (Carleton University), $A$(rthur)-Packets of Cohomological Representations 9:00 - 9:30 Ed Belk (University of British Columbia), The Local Trace Formula as a Motivic Identity 9:30 - 10:00 Daniel Le (University of Toronto), mod $p$ representations of $p$-adic $\mathrm{GL}_2$ 10:00 - 10:30 Boaz Elazar (University of British Columbia), Schwartz Functions And Tempered Distributions On Singular Quasi-Nash Varieties 16:00 - 16:30 Adele Bourgeois (University of Ottawa), On the Multiplicities in the Restriction of a Supercuspidal Representation 16:30 - 17:00 David Roe (Massachusetts Institute of Technology), A database of p-adic tori 17:00 - 17:30 Nicole Kitt (University of Calgary), An ABV-packet for a General Linear Group with Two Representations 17:30 - 18:00 Loren Spice (Texas Christian University), New developments in the construction of tame, supercuspidal representations Sunday June 9  (ED 312, Education Building) 8:30 - 9:00 Qing Zhang (University of Calgary), local converse theorems for unitary groups 9:00 - 9:30 Joshua Lansky (American University), Explicit liftings of conjugacy classes in finite reductive groups 9:30 - 10:00 Wan-Yu Tsai (University of Ottawa), The orbit philosophy for Spin groups 10:00 - 10:30 Hadi Salmasian (University of Ottawa), The minimal faithful dimension of finite p-groups: an application of the orbit method to the essential dimension STUDC Research Session Sunday June 9  (CK 185, Centre for Kinesiology) 8:00 - 8:30 Curran McConnell (Dalhousie University), Combinatorics of spaces of trees: an application of topology to phylogenetics 8:30 - 9:00 Asmita Sodhi (Dalhousie University), Integer-valued polynomials and a game called $p$-ordering 9:00 - 9:30 Nicole Kitt (University of Calgary), How to calculate perverse sheaves on quiver representation varieties of type A 9:30 - 10:00 Anne Dranowski (Univeristy of Toronto), MV cycles from generalized orbital varieties 10:00 - 10:30 Peter Bradshaw (Simon Fraser University), Cops and robbers on Cayley graphs The Mathematics behind Quantum Information Science Org: Nathaniel Johnston (Mount Allison) and Sarah Plosker (Brandon) Saturday June 8  (ED 230, Education Building) 8:00 - 8:30 Vern Paulsen (University of Waterloo), Constant Gap for Self-embezzlement 8:30 - 9:00 Mizanur Rahaman (University of Waterloo), A new bound on quantum Wielandt inequality 9:00 - 9:30 Nathaniel Johnston (Mount Allison University), Pairwise Completely Positive Matrices and Quantum Entanglement 9:30 - 10:00 Sarah Plosker (Brandon University), The robustness of $k$-coherence 10:00 - 10:30 Eric Chitambar (University of Illinois Urbana-Champaign), Playing Mermin’s Game with Nonlocal Resources 16:00 - 16:30 Rupert Levene (University College Dublin), Schur multipliers and mixed unitary maps 16:30 - 17:00 Jeremy Levick (University of Cape Town), Factorizable Quantum Channels and Linear Matrix Inequalities 17:00 - 17:30 Rajesh Pereira (University of Guelph), Quasiorthogonal algebras 17:30 - 18:00 Sabine Burgdorf (University of Konstanz), Quantum correlations and optimization Sunday June 9  (ED 230, Education Building) 8:30 - 9:00 Gilad Gour (University of Calgary), Theories of Dynamical Quantum Resources 9:00 - 9:30 Carlo Maria Scandolo (University of Calgary), Necessary and Sufficient Conditions on Measurements of Quantum Channels 9:30 - 10:00 Jason Crann (Carleton University), State convertibility in the von Neumann algebra framework. 10:00 - 10:30 Comfort Mintah (University of Guelph), Operator algebras and quantum one-way LOCC state distinguishability 16:00 - 16:30 Neil J. Ross (Dalhousie University), A Characterization of Integral, Real, and Gaussian Clifford+T Operators 16:30 - 17:00 Sam Harris (University of Waterloo), Separating the matrix-valued bipartite correlation sets 17:00 - 17:30 Jamie Sikora (Perimeter Institute), Shadow Probabilities 17:30 - 18:00 Satish Pandey (Technion) Topology Org: Martin Frankland, Donald Stanley and Paul Arnaud Songhafouo Tsopméné (Regina) Saturday June 8  (ED 318, Education Building) 8:00 - 8:30 Robin Koytcheff (University of Louisiana at Lafayette), The Taylor tower for the space of knots and finite-type knot invariants 8:30 - 9:00 Robin Koytcheff (University of Louisiana at Lafayette), Operadic decompositions of spaces of string links 9:00 - 9:30 Laura Scull (Fort Lewis College), Transitive Groupoids with Interesting Topological Properties 9:30 - 10:00 Jeffrey Carlson (University of Toronto), Local integration in equivariant cobordism theory 10:00 - 10:30 Rachel Hardeman (University of Calgary), An Introduction to A-Homotopy Theory: A Discrete Homotopy Theory for Graphs 16:00 - 16:30 Ben Williams (University of British Columbia), $\mathbb{A}^1$-homotopy and a conjecture of Suslin 16:30 - 17:00 Steven Rayan (University of Saskatchewan), The quiver at the bottom of the twisted nilpotent cone on $\mathbb P^1$ 17:00 - 17:30 Cihan Okay (University of British Columbia), Mod-$\ell$ homotopy type of the classifying space for commutativity 17:30 - 18:00 Anthony Bahri (Rider University), Polyhedral products and their applications Sunday June 9  (ED 318, Education Building) 8:30 - 9:00 Tyrone Ghaswala (University of Manitoba), Promoting circle actions to actions on the real line 9:00 - 9:30 Patrick Naylor (University of Waterloo), Trisections and twists of 4-manifolds 9:30 - 10:00 Kate Poirier (New York City College of Technology), Directed planar trees, V-infinity algebras, and string topology 10:00 - 10:30 Krishanu Sankar (University of British Columbia), Mod 2 cohomology and the braid group


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# Replacing the contravariant Minkowski metric tensor by its inverse

From Wikipedia, the Minkowski metric is defined (using (- + + +) signature) as : $$\eta_{\mu \nu} = \eta^{\mu \nu} = \begin{pmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$$

I am a beginner in tensor calculus, and feel uneasy that a covariant vector is being equated to a contravariant vector. Is it then possible to simply replace the covariant Minkowski metric tensor by its contravariant counterpart withing a calculation ?

For example, given a four vector $$k$$, is it correct that :

$$k \cdot k = \eta_{\alpha \mu}k^{\mu} k^{\alpha} = \eta^{\alpha \mu}k^{\mu} k^{\alpha}$$

Are there any problems with summing over all upper indices ?

It's important to understand that the statement

$$\eta_{\mu \nu} = \eta^{\mu \nu} = \begin{pmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$$

Does not say that the metric is equal to the inverse metric. Such a statement doesn't even make sense, because the metric and inverse metric are tensors which eat different kinds of objects (vectors in the former case, covectors in the latter).

What is says is that, in the particular basis which you have chosen, the components of the metric (which are just real numbers) are equal to the components of the inverse metric (which are also real numbers).

[I] feel uneasy that a covariant vector is being equated to a contravariant vector

A covariant vector is never equal to a contravariant vector, because those two objects live in different spaces. The components of a covariant vector (in a particular choice of covariant basis) may or may not be equal to the components of a contravariant vector (in a particular choice of contravariant basis), but that is a vastly different statement (which of course depends on which bases we intend to use).

You can do it in this particular case, because that matrix is its own inverse; the components of $$\eta_{\mu\nu}$$ and $$\eta^{\mu\nu}$$ are the same. This doesn't happen in general, so it's basically the only case where you could replace downstairs indices by upstairs indices (though you shouldn't, because it's confusing).

Hint: Inverse of a diagonal matrix is inverse of each entry along the diagonals. Can you see why the components of inverse metric is just inverse of components metric here i.e. $$\eta_{\mu\nu} = \eta^{\mu\nu}$$?

Given a four vector you may think of $$k^{\mu}$$ as a column vector, and $$k_{\mu}$$ as a row vector. I think that will help you see why $$\eta_{\alpha \mu}k^{\mu} k^{\alpha} \ne \eta^{\alpha \mu}k^{\mu} k^{\alpha}$$.

What is true is the following: \begin{align} k_\mu \cdot k^{\mu} &= \eta_{\mu\alpha}k^{\alpha}k^{\mu} \\ &= \eta_{\mu\alpha}(\eta_{\mu\alpha}\eta^{\mu\alpha})k^{\alpha}k^{\mu} \qquad \qquad (\because \eta_{\mu\alpha}\eta^{\mu\alpha} = \mathbb{I})\\ &= \eta^{\mu\alpha}(\eta_{\mu\alpha}k^{\alpha})(\eta_{\mu\alpha}k^{\mu}) \\ &= \eta^{\mu\alpha}k_{\mu}k_{\alpha} \end{align}


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## Cryptology ePrint Archive: Report 2014/687

Reducing the Complexity of Normal Basis Multiplication

Omer Egecioglu and Cetin Kaya Koc

Abstract: In this paper we introduce a new transformation method and a multiplication algorithm for multiplying the elements of the field GF$(2^k)$ expressed in a normal basis. The number of XOR gates for the proposed multiplication algorithm is fewer than that of the optimal normal basis multiplication, not taking into account the cost of forward and backward transformations. The algorithm is more suitable for applications in which tens or hundreds of field multiplications are performed before needing to transform the results back.

Category / Keywords: implementation / Finite fields, characteristic 2, normal basis, optimal normal basis


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# Lynx eat snowshoe hares and snowshoe hares eat woody plants like willows. Suppose that, in the absence of hares, the willow population will grow exponentially and the lynx population will decay exponentially. In the absence of lynx and willow, the hare population will decay exponentially. If $L(t), H(t),$ and $W(t)$ represent the populations of these three species at time $t,$ write a system of differential equations as a model for their dynamics. If the constants in your equation are all positive, explain why you have used plus or minus signs.

## see above

#### Topics

Differential Equations

### Discussion

You must be signed in to discuss.

Lectures

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### Video Transcript

it was for So we know that means we eat snowshoe hares and a social hairs eat, we lose or care. So there to situations The first one says, um, that hairs are not president. So this is true. Then we want to see how the links and wills well, how the wings be here. So you could write down the director derivative off the wills respected Time is going to equal to que times w minus k times. So this is true because the here the Williams will grow exponentially. That's why it's a positive. It w and then the limbs will dig caves full. Actually, that's really we have the negative K times. So Ah, the second situation is that the links and there would low are not present. This is true. We want to see how the, um Harris change with time so we could write down derivative off h respected time. And then h is, um here's so what will happen to them? Well, we know that the hair publisher will be care exponentially so we could write need okay times each. And that is a

California State University - Long Beach

#### Topics

Differential Equations

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## Number operator help

I am sorry I don't know what you mean, is it like $N/V = \int (\frac{1}{(2\pi)^3}) d^3 k d^3 k' a^\{dagger} a = \int (\frac{1}{(a2\pi)^3}) d^3 k a^\{dagger} a$
 so as in the Volume cancels with the second d^3 k' term?
 N=Ʃk a+a=V/(2∏)3∫d3k a+a,V is volume.

 Tags 2nd quantisation, fermionic n operator, number operator


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# Single-Token Pool

Many project owners face the following problems when using AMMs to provide liquidity:
• You must have project-side tokens to provide liquidity
• Buying project-side tokens requires good liquidity
To solve these problems, project owners must rely on a complex issuance process. Whether it's an auction, liquidity mining, or providing initial liquidity themselves, it takes up a lot of the project owner's energy and increases the barrier to user participation.
DODO has created a unilateral initial liquidity solution to make the whole process simple, called the Single-Token Pool model. Let's see how it works.

### DODO's Single-Token Pool Model

A Single-Token Pool can be compared to a vending machine that allows you to return assets purchased from it. The more units you buy, the more expensive each one becomes. The money you pay for the goods is stored in the pool, and when you don't want the assets you purchased, you can return them at the current price.
The price curve of a Single-Token Pool is defined by the PMM algorithm as a price curve with a minimum price, which is the price of the first item purchased from the pool.
Anyone can set up a Single-Token Pool and set the variety of goods it contains. You can set it up with mainstream assets like BTC and ETH, or with new assets that you issue yourself.
You don't need to provide any denominated assets at first, just fill the vending machine with goods. This design allows you to create ample liquidity for your tokens on DODO, without spending a dime, in just 5 minutes.

### Similarity to AMMs

If a Single-Token Pool is created with the slippage factor
$k=1$
and the guide price
$i$
is a very small number, then it behaves almost the same as an AMM. You can think of the Single-Token Pool curve as an AMM price curve that truncates the parts that are smaller than
$i$
. The smaller
$i$
is, the closer it is to a true AMM curve. This can be accomplished by setting
$i=0.000001$
.

### Anyone Can Participate

Anyone can supply the Single-Token Pool with both sides' assets to participate in the liquidity supply, just as with an AMM. The difference here is that the value of the two assets need not be 1:1 when resupplying.
Anyone can participate in adding liquidity, which is these pools are sometimes referred to as public pools.

## Use Cases

### Build Initial Liquidity for High Volume Markets

Suppose you are a blockchain developer and want to build a community-driven project. You can issue 10 million tokens, of which 1%, or 100 thousand, are reserved for the project team. The rest (i.e. 9.9 million tokens) are distributed to the community.
Let’s say you set the token price to $1. If you want to create a liquidity market for all 9.9 million tokens on an AMM, you need another$9.9 million as the bid-side liquidity to do it - a huge amount of money that you probably don’t have, and so this project becomes infeasible.
Your alternative is to create a simple AMM pool with much fewer tokens and less liquidity in it, say $1,000 and 1,000 tokens, but if someone wants to invest$100,000 in your project token, he will have to pay $100,000 and receive only 1,000 tokens in return. This amounts to$100 per token, 100x the market price you set! This is, of course, not desirable, and this market is definitely not an efficient market.
However, you can choose to build a Single-Token Pool with these 9.9 million tokens at an initial price of $1 and with the k value set to 1. If a community member is bullish on your project and buys 100,000 tokens, his average price is only$1.005 per token!

### Raising Liquidity Fast

Imagine, for example, an algorithmic stablecoin project whose USD-pegged coin has dipped below $1. The project needs to raise liquidity as soon as possible to prevent a death spiral. If you can reverse the price decline at$0.9, it will greatly strengthen market confidence, but if it reverses only at \$0.5, it may have led to a permanent loss of confidence in your token.
This hypothetical project has an easy solution to its woes! Suppose the project token is called X. Create a DAI-X pool, set the guide price to 1, and
$k=0.01$
. In addition, you incentivize liquidity providers to deposit their LP tokens into this pool with rewards in X. This way, you can ensure ample bid-side liquidity that is allocated near 1 X = 1 DAI, which is a much more capital-efficient funding model than traditional AMMs.
Even if it’s not an algorithmic stablecoin project, you can still raise funds for your token at key support price levels with Single-Token Pools, coupled with a reward incentive program to encourage liquidity provision.


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# CodeIgniter use model from model's constructor

I have two models, first one is dependent on the second one, and I need to call methods from the second one in the first one's constructor.

So far I have this:

user

class User extends CI_Model {

protected $_attributes = array(); function __construct() { parent::__construct();$this->load->model('musers');
foreach($this->musers->GetProfile() as$key => $val) {$this->_attributes[$key] =$val;
}
}

function __set($key,$val) {
return $this->_attributes[$key] = $val; } function __get($key) {
return $this->_attributes[$key];
}
}

I have put this model in the autoload config file and here's what I get:

A PHP Error was encountered
Severity: Notice
Filename: models/user.php
Line Number: 20

Fatal error: Call to a member function model() on a non-object in  path\to\models\user.php on line 9

There's also something strange - the first error (notice) refers to line return $this->_attributes[$key]; while it surely should reference line $this->load->model('musers');. I have tried loading model musers in autoload before the user model, but nothing helps. I have tried searching for this, but could not formulate the query well, I'm sure there are solutions to my problem. As I understand this is because the constructor of the second model is called before CodeIgniter manages to load the loader class itself, but that's pretty odd. - ## 2 Answers Try: function __construct() { parent::__construct();$CI =& get_instance();
$CI->load->model("musers", "musers"); foreach($CI->musers->GetProfile() as $key =>$val) {
......
}

......

-
You, Sir, are my today's hero, kudos to you! Didn't think of it, despite the fact I'm constantly writing libraries nowadays. –  Sergey Telshevsky Sep 6 '12 at 11:49
@Vlakarados glad you got it... :) –  Sudhir Sep 6 '12 at 11:58

Try like this

$CI = &get_instance();//you need to define the instance for loading the second model musers$CI->load->model('musers');

-
Thank you! A bit late to be the first though :) –  Sergey Telshevsky Sep 6 '12 at 11:51


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Free Version
Moderate

# Area: Equilateral Triangle

GEOM-H4HYLA

Each side of an equilateral triangle has a length of 6 inches.

Find the area of the equilateral triangle in square inches.

A

18

B

$9\sqrt{3}$

C

$18\sqrt{3}$

D

$6\sqrt{3}$

E

$36\sqrt{3}$


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By James W. Burdick (republished with the author’s permission)

So, I’m at Costco yesterday, deep in the Bloomfield Hills ghetto, where everyone knows how dangerous a place it is. Uh. And I see this kid — maybe 25, wandering through like other shoppers. Except he had no shopping cart or purchases in his arms, but he was strapped with a shoulder holster and small automatic in “open view.” . . .

My first instinct is to ask if he’s expecting trouble. But he stared at me so innocently and so clearly frightened at his own silliness, all I could think was, the first bad ass who jumps up in his grill is going to take that gun away from him and shove it where the sun don’t shine.

I’m pretty sure he’s never seen a gangbanger close up, or a drunk or a tough guy high on PCP. I can just tell he truly has no idea what he’s doing, or maybe even why. But I’m also thinking, he’s actually making MY favorite Costco dangerous for others for no good reason, since I just can tell he’s not trained in law enforcement or military use of weapons. And while I don’t care if he gets himself killed, I do care if he gets some totally innocent person killed because he wants to feel like a big man.

So shame, shame on the cowardly politicians who rained this insanity upon us for no reason other than to do the bidding of the gun manufacturers masquerading as “second amendment” zealots.

Anyone with a brain can read the word “militia” right there in the Second Amendment and know it’s not about this little guy having the right to take a fucking pistol into Costco in the middle of a Saturday afternoon.

James Burdick, a former Wayne County prosecutor, is a criminal defense attorney who also handles health care cases at Burdick Law, P.C. in Bloomfield Hills.

#### 125 COMMENTS

• Nothing to see here; just another venomous anti-gun dinosaur projecting the memories of his own inadequacies at that age onto others.

When HE was that old, there weren’t very many places to get good personalized defensive handgun training (maybe only Gunsite?), no Internet to learn from others’ mistakes and pick up carry/training tips, and no DVDs/videos to assist in self-training, so he assumes that everyone else is as clueless as HE was at that age.

• As a lawyer, there is nothing I detest more than people who graduated from non-third-tier-toilet schools and who spout off legal arguments that have been clearly rejected by the Supreme Court. It’s on par with a Southern DA citing Dredd Scott to support his worldview.

• He’s obviously caught Andrew Dice Clay’s act though, with a lead-off like that. I had to go back and make sure he wasn’t in the line at the bank.

Butch it up any way you need to skippy.

• And reading his article, it is clear that he has never read Heller or McDonald, and has forgotten how long Michigan has been an open carry state, even though he purports to be a Super Lawyer and a criminal defense lawyer at that. In my town, most of the criminal defense lawyers have CCWs.

• ” In my town, most of the criminal defense lawyers have CCWs.”

I know a handful of lawyers here in Florida and like you they are gun guys.

Probably because by interacting with criminal defendants they grasp the concept of the need for self-defence.

One in particular has a very nice collection that he has been building by taking guns as payment for his services.

As soon as they plead out they can’t own them anyway…

1. Well, Mr. Burdick, when I go to Costco, I carry a “fucking pistol”, also. Every damn time!

• I wonder if concealed carriers make him feel this way? Or just those open carrying. If concealed handguns in untrained hands are just as dangerouse then maybe he always feels that way since you can’t always tell who is and who is not carrying? Do cops make him feel that way? Licensed carriers of fire arms are LESS likely to commit a crime than police. And I don’t want to downplay police or military training BUT military training to use a defensive handgun is minimal and police training for most officers is bare. Most officers have never fired their gun at a suspect and many when they do hit innocents ( see NYPD). Now sure te guys on swat teams train all day, but most cops are not trained anywhere near that level. They et a few days at the academy the. Qualify 2 times a year for the next 30 years.

2. Pretty pathetic transfer of fear and ignorance. I would expect better from him with a real argument.
Sorry he didn’t provide a photo of said scared kid. Then again maybe that child didn’t exist at all except in his own mind.

3. 25 year old ‘kid’
Is he serious?
What would these people set as the age to be permitted all of your human rights? 30? 35?

• You are allowed your rights if you are within one nanosecond of his age, or (quite generously!) within one nanosecond of the age of any of his progtard friends.

Otherwise, you can fvck off and die.

(/sarcasm, if it’s not obvious.)

• When I was a 25 year old innocent looking young man, I was 4 years a veteran of the Army’s Infantry Program For Wayward Boys. I’ve seen some shit that I hope this man will never have to see. When I come, I always come prepared.

• I’m younger than this ass hole and I would call 25 year old a kid. Of course I might be saying go get yourself a gun kid and learn how to use it. The world is a dangerouse place and you can’t count on anybody else to protect you.

• The people ARE the militia. This doesn’t mean you have to be militia to qualify as “people”.

• Because it allows them to use the “well regulated” part which has evolved to mean “government control.” Without that, they couldn’t (cough, cough) rationalize their power grab. Even the most horrible dictators used “legal fig leaves” of tortured language to justify their atrocities.

4. the US Supreme Court makes the distinction between the militia clause and the RKBA clause of the 2nd Amendment. How is it this lawyer cannot?

5. the first bad ass who jumps up in his grill is going to take that gun away from him and shove it where the sun don’t shine

If that’s true, why didn’t you try it? Probably because you knew that the young man would put two into your empty cranial cavity before you could blink.

Why is it that present and former .gov scum think that they’re smarter than anyone else, when it fact, they don’t know sh1t but they do enjoy talking out of their asses.

• To be fair, he might have not tried it because most people (even pro-disarmament jackasses like this one) simply don’t go around assaulting other people, just to see if they can.

Also, he did say “the first bad ass”, and Burdick is almost surely not that.

• I understand their narcissistic delusion of being smarter than everyone else. It’s the Ms Cleo like ability of seeing the outcome of hypothetical events that makes me question their sanity.

• He runs his mouth pretty ragged for a msn that dont go heeled.

Skin that smoke wagon and go to work!

6. Didn’t an Air Force Major get gunned down by some cops outside a Costco a few years ago?
He was asked to leave when a boxboy or something saw his pistol peek out from under his jacket. He left after talking to the manager and ran into the cops outside the store. Officer one shouted to get on the ground, officer two shouted to show him the weapon. The victim followed ofc. 2’s instruction and ofc. 1 lit him up. Naturally ofc. 2 joined in. Inquest ruled it justifiable, as usual.

My point being, Costco forbids weapons on the property. So I call B.S.

• I call BS because what is a supposedly white, well educated, rich lawyer doing in a bad part of town, at costco no less.

• He was being fecitious in calling Bloomfield Heights the “ghetto”, and he possibly also being a bit of an elitist braggart. Bloomfield is literally one of the 5 richest towns in the entire country, as in all or the USA, 39% of the homes are >$1M. • “Militia” I do no think that word means what Mr. Burdick thinks it means. He like all the anti-gunners misses the entire point of 2A. Which is: There can be no well regulated militia without guaranteeing the people’s right to keep and bear arms. If the people do not have that right, a well regulated militia can not exist. • That was my first thought, Costco’s membership agreement states that you cannot carry firearms in their store. So I’m calling shenanigans on open carrying in Costco. This guy, in my opinion, is not being honest. I am not a member, so I never signed an agreement, they do not post per state law, so I carry CONCEALED when I go with someone close to me who has a membership card. If they ever do kick me out, I’m not out anything cause I don’t pay their dues. 7. Headline’s being a bit charitable to the author. It sounds like Burdick doesn’t like the idea of any carry, and probably isn’t too thrilled about “letting” the little people own guns at all. 8. DON’T SCREW WITH A MAN’S FAVORITE COSTCO ! His Constitutional rights, sure, But not that. 9. Anybody who’s worked in the Wayne County Prostitute’s Office has earned my eternal scorn. Let me guess, he’s one of the jackhandles who used tax dollars to sue gun makers for making guns back in the 1990s. 10. He is absolutely correct about “[a]nyone with a brain can read the word “militia” right there in the Second Amendment and know it’s not about this little guy having the right to take a f-cking pistol into Costco . . ..” However, the sentence is irrelevant to the article as open carry is separate from the militia reference in the 2nd A. This red herring seriously distracts from the main thought of his article; he is uncomfortable. Uncomfortable? You have no right to not feel uncomfortable. Lose the ego. What would a prudent person interested in helping the lad do? How about introduce yourself? Strike up a pleasant conversation to get a better understanding of the fellow. Based on how that goes, discuss how training is helpful regardless of one’s experience or notify the appropriate authorities of a problem. The gist is to be helpful to reduce the kid’s perceived inexperience while addressing the safety to the public you allege motivated you to write the article. In this manner, you may make a more positive difference in the world. Carry on. • Yes, I just KNOW what people are like when I look at them on the street… “I believe he’s never seen a tough guy close up, or a drunk or a tough guy drunk on liquor or pcp. So I know he has no idea what he’s doing…” Just like this Burdick KNOWS the young man has no idea what he’s doing…It would be interesting to know how much experience Burdick has with TRULY tough guys who look pretty unassuming. I’ve met some combat instructors in my younger days who didn’t look like much, but they had all the street cred for ACTUAL violent confrontations that this Burdick lacks. Unless he’s telepathic…yeah, that’s the ticket! • Well, duh! Of course he is telepathic. Didn’t you know that?! It is common knowledge that statist/leftists are all-seeing and all-knowing. If we would just surrender to their enlightenment, we would be so much better off for it as they know what is best for us more than we do. Freedom of thought is such a messy process. You know it would be so comforting to have an older sibling with that kind of oversight. You know, like a big brother. We would all be so much happier. (/sarc) 11. Just think: this mental giant with self-esteem and projection issues used to get to use the power of the state (and purse of tax collectors) to compensate for those shortcomings. I would not be surprised to find out that this jackwagon would attempt to throw the book at people like the law-abiding open-carry Bogeyman in his story, while putting the gangbangers he referenced in that same story through the revolving-door, catch-and-release system. • Mr. Burdick IS an Operational Operator Operating Operationally. He even has the Arrow to the Knee Medal and is authorized to wear a chocolate “S” device on his associated ribbon for valerterious Self-Infliction. Kid w/the Don Johnson probably figured Mr. Sweaty crotch was going to SWAT him. 12. Make ASSumptions, go ahead. That 25 something make be a SOF operator, a competitor, or a citizen well within their rights. I call BS on this guy, for projecting his own prejudices. I prefer concealed carry, but I have open carried on occasion. In Pennsylvania the only comment I ever got was at a Sheetz when a State Trooper commented on my Sig 1911 Scorpion and how much he liked the kydex holster. 13. He thinks he can size someone up that easily because he’s dealt with people in court? For all this idiot knows, that “kid” could have just come back from a combat tour in Afghanistan and/or be an IDPA competitor with a black belt, who could kick his ass and a gangbanger’s ass, both at the same time. You never judge a book by it’s cover when you’re dealing with those kinds of issues. The kid could look frightened because his wife sent him to Costco to get something and he has no earthly idea where in the store it is! I have been there! This bozo was a prosecutor in an area that has become a shooting gallery and where the city of Dearborn has been all but taken over by Islamic extremists. Why isn’t this lame-o speaking out his office’s shameful lack of performance, instead of dissing some law-abiding citizen about ruining “his” Costco, like Costco is a place you go for the ambiance! The Detroit police chief next door is encouraging people to carry guns and use them. The chief is at least admitting Detroit/Wayne County is out of control. 14. …since I just can tell he’s not trained in law enforcement or military use of weapons… LoL. The other day I stared at a rock that randomly picked up off the ground and I just knew it – just knew it – that there would be a diamond inside of it. I could tell just by looking. Anyone with a brain can read the word “militia” right there in the Second Amendment and know it’s not about this little guy having the right to take a fXXing pistol into Costco in the middle of a Saturday afternoon. “I ask, sir, what is the militia? It is the whole people, except for a few public officials.” — George Mason 15. Anyone with a brain cell can see the words, “the right of the people to keep and bear arms, shall not be infringed.” Anyone with two brain cells knows what that means. 16. Little Jimmy used to be a country prosecutor and now he is a criminal defense attorney who also takes health care cases. His mastery of suppostion and conjecture must have served him well his previous occupation and his ability to deny reality must be an indispensible asset in his current law practice. I bet he is a lot of fun to watch in a courtroom. • Little Jimmy used to be a county prosecutor Probably where he learned to play fast and loose with the truth. 17. The words of a frightened, closed-minded man who THINKS he understands more than he actually does. 18. He needs to read what the founding fathers wrote about what is the militia and the Militia Acts of 1792. 19. He edited out all the F bombs he had in the original article. Also, he graciously pulled strings to get himself a Michigan carry license back when the little people couldn’t get them. He’s a retired control freak who is no longer in control and is having a difficult time adjusting. 20. I will take what Mr Burdick related ( since none of the other commentators did it fairly), and add that I believe ( I say again) that open carry is probably constitutional, but people who open carry are reckless for many reasons, not the least of which is that he (or she) will be the first one shot by the bad guys or by the police if trouble occurs. 21. I love the police and military training canard. They act like you have to have some super special Hogwarts like training to handle a weapon only available to pure blood government cronies. • Indeed. So the “kid” didn’t have police or military weapons training (how can you tell that just by looking at someone)? So what? The “kid” isn’t carrying so he can enforce the law or engage enemy combatants in Costco. He’s carrying so he doesn’t get mugged on his trip to buy 96 rolls of toilet paper and a 5-gallon bucket of mayonnaise. 22. Oh look, yet another person who knows better than me. It’s so comforting to know that there are so many of them out there, otherwise I just couldn’t take care of myself! P.S. I’m loving the irony of this guy talking about that 25 year old trying to be a tough guy while he, the supposedly even tougher dude, did/said nothing at the time besides run home and write an angry tough guy letter. Priceless. 23. I’m wondering if this even happened. I don’t believe it’s possible to open carry in a Costco. I’d assume you’d be asked to leave the store. From Costco’s website: “Costco does not believe that it is necessary for firearms to be brought into its warehouse stores, except in the case of authorized law enforcement officers. For the protection of all our members and employees, we feel this is a reasonable and prudent precaution to ensure a pleasant shopping experience and safe workplace. Our policy is meant to protect our members and employees in all warehouses around the world.” • I open carry when riding my motorcycle. Never had any problems when gassing up at Costco. I conceal my pistol when going into the store, however. • That’s a damn good reason NOT to shop at Costco. Does Sam’s have the same policy? • I don’t know of such a policy, and the fact that they’re owned by Walmart, which “follows state law”, would indicate that the answer is probably that there is no such policy. 24. The Second Amendment is all about the “little guy”, James. Even f%^$tards like you.

25. He must have been confused. Costco would have booted him ASAP due to their fine print policy on guns. I think since he was a prosecutor, he must be a liar.

26. Without law enforcement or military training? I’ve got some news for you, the best weapons retention training you’re going to get in the world doesn’t come from BCT or any law enforcement school. I’m not even a huge advocate of open carry, but this guy is a prat. Who does he think he is to tell anyone what right they have?

My bet is that apparently he has enough money to have landed himself a house in Bloomfield Hills, and thus as one of the elite, doesn’t think the plebs should be carrying handguns in his beloved Costco. Later granddad, your sun has officially set.

27. That’s a lot of quick judgment heaped on a law abiding open carrier. And it’s not YOUR Costco, Jim.

28. Sure jumps to some conclusions kinda quick.
How does Mr. Burdick know the guy WASN’T in a militia? And hadn’t received hundreds of hours in training?
And the look of fear in his eyes was the fear that he was going to have to shoot “yet another” dummy…

29. James Burdick Doesn’t Like Open Carry.

The Mr Burdick should refrain from doing so.

Not sure where he go the idea that what he wants has any bearing on anyone else but whatever.

30. Three things occur to me: 1. Did this “kid” even exist at all or is he just a straw man? 2. If “kid” did exist, I doubt this mans ability to judge his training, background, or ability to utilize said automatic by observing a stroll through Costco. 3. This reinforces my opinion of lawyers in general (yes we all know exceptions – including some who post here that are truly exceptional).

• I had similar thoughts. Years ago, as a teenager, we had a friend of the family who was a detective on our Houston suburb’s police department. It’s not HPD, but they’d get their share of crime, I suppose, even the occasional homicide.

We’d get to talking and he’d tell me about cases, sometimes interrogations, and how he could tell whether someone was lying. A big part of it is just the mystique of homicide detectives and that they might just be able to tell. So they bluff and get you to confess.

There is an actual art to it, though, and there are some techniques. One is keying in on how a suspect/witness recounts the events. There are no guarantees or one size fits all approaches, of course. Still, a story told in the present tense is more likely to be fabricated right there on the spot, than one told in the past tense. Same goes for a story with awkward “I” and “my” references, suggesting the teller wasn’t just an observer, but is the creator of the story.

This lawyer alternates between past and present tense. He calls the store “my” Costco. Could just be his style. Could just be him trying to keep it breezy sounding (like his use of slang such as “grill”), so he doesn’t come off as a bitter old white guy. Or it could be him making the whole damn thing up.

I don’t know that he’d be any less pathetic if it actually were true, though. So I guess it’s a moot point.

31. From the original article:
“So I know he has no idea what he’s doing, but that he also probably has a very tiny wee-wee, which explains the gun.”

Now we’re back to the penis-size-ratio argument – AGAIN!

32. One of the “elites”, ANGRY, ANGRY I tell you, that one of the little people, not anointed and blessed by the Powers That Be with a special little shiny piece of metal is OC’ing a gun.

Anger is usually based in some type of fear. I believe Burdick is scared of the peasants not bowing and scraping for permission from people like him to exercise what he thinks should be a privilege, which he would never give.

33. He now handles health care cases? So he’s a freaking ambulance chaser. The cost of health care in this country is at least double due to scum bag lawyers like this guy. I wonder how he feels about tort reform?

34. “since I just can tell he’s not trained in law enforcement or military use of weapons”. I just laughed so hard that I snorted.

35. If the story is factual, I’d bet it was a black “kid” and the “fair” former prosecutor was doing a bit of racial profiling. Anyway, what’s this rich lawyer doing deep in the ghetto anyway – shopping for those $5 whole baked chickens? • I posted this above in response to a similar comment: He was being fecitious in calling Bloomfield Heights the “ghetto”, and he was possibly also being a bit of an elitist braggart. Bloomfield is literally one of the 5 richest towns in the entire country, as in all of the USA, 39% of the homes are >$1M.

36. Side Note:

As of 2010, former and retired prosecutors qualifiy for a concealed weapons permit.

Apparently he just hates the “little pebbles” have access to things only the enlightened few should have.

37. “I’m pretty sure he’s never seen a gangbanger close up, or a drunk or a tough guy high on PCP. I can just tell he truly has no idea what he’s doing, or maybe even why. But I’m also thinking, he’s actually making MY favorite Costco dangerous for others for no good reason, since I just can tell he’s not trained in law enforcement or military use of weapons. ”

[sarcasm]This guy can really make a dent in court costs. All they have to do is put the defendant in front of him and he knows wether he is guilty or innocent. No need for a trial.[\end sarcasm]

“And while I don’t care if he gets himself killed”

Very Christian of him.

38. Ahh, yes. A former Detroit prosecutor that apparently doesn’t live in the city anymore….and lives in west bloomfield. Perfect.

I love personally, how open carry, which has been legal in the state of Michigan since it became a state, is somehow “the politicians giving into the gun lobby” (or whatever the quote was…).

It does seem that this particular open carry dude wasn’t exactly giving off a good vibe: shoulder holster for OC tips me off( but it shouldn’t….who am I to judge?)

I’m sure he was ocing because of Costco’s anti gun stance…not that that is bad either…..

• Anyone up for a road trip to stand on the public right-of-way outside of Herr Burdick’s office with openly visible firearms?

39. Short version of Mr. Burdick’s rant, “I am superior and hate ‘inferior’ people … and therefore reject the notion that ‘inferior’ people have any rights. In fact I reject the notion that ‘inferior’ people have any inherent human dignity whatsoever.”

People like this douchebag are the very reason that I am armed.

• Of course the idea that anyone else is inferior to him is all in his mind. Probably helps him to inflate his ego even further to imagine all the inferior people he sees every day.

40. John F.’s comments are mine as well. The writer comes across as ageist. Men at 18 can join the military, be trained in shooting, and use a rifle in combat. The man with the rifle could be a veteran with multiple tours of duty overseas. He could have used his rifle a lot and has relatively little experience with a handgun. He might be more comfortable shooting a rifle than a handgun. The author may not like the ascetics of a man carrying a rifle, but it is his right and his preference for a tool of self-defense.

Many states do not allow someone younger than 21 to carry concealed, but open carry is allowed. It is completely closed minded to believe that those 25 and younger cannot be responsible and carry firearms to protect themselves and their families. Whatever happened to the pleas of accepting those who are different. The author may not understand or accept the person’s motivations, but is important to recognize that the open carrier’s beliefs are protected and respected by our society. I find it so sad that tolerance and understanding are rarely applied to gun owners.

41. “I’m pretty sure he’s never seen a gangbanger close up, or a drunk or a tough guy high on PCP….”
And I’m positive I can’t tell squat about someone from just looking at them. Politicians look like descent human beings yet the only thing I would be sure of is they are mostly lying thieves.

42. As usual, the comments here are as mindlessly predictable and unreasoned as Shannon Watts. You all sound like irresponsible, self-entitled, six year old children. “It’s my right to do whatever I want, and nobody can make me stop.” Wrong! Society does have a say in how you can keep, and bear arms. I live in Florida, and have for 30 years, and this state says you can carry a firearm, you just have to carry it concealed. I don’t feel infringed, and it gets pretty damned hot down here in the summer months, when carrying concealed becomes more than just a little uncomfortable. BFD.

In this article, here’s where most of your childish protestations about open carry go off the tracks. Is a shoulder rig designed for a) open carry, or b) concealed carry? If any of you didn’t already know, it is b) concealed carry. So why is the jerk in Costco walking around with one openly? Is it because a) he wants everyone to see him carrying it, or b) he wants everyone to see him carrying it, or c) both a and b?

“You’d bury yourself alive just to prove you can handle a shovel.”

• Society does have a say in how you can keep, and bear arms.

Actually, no society doesn’t. The right is natural, endowed by our Creator, and unalienable. Further, the right is constitutionally protected against infringement, by anyone.

Your premise therefore is false.

• To say nothing of the fact that open carry, as noted by someone else above, is and has been perfectly legal in Michigan for a very long time–that it has fallen out of fashion is irrelevant. Which of course this jack wad knows (or at least should know) because of his experience as a prosecutor and now criminal defense attorney. Strange how he conveniently omits that fact from his diatribe, instead preferring to blatantly lie by stating that open carry is the result of recent actions by gun nuts and the NRA. Add to that the fact that he has not bothered to read Heller or McDonald as to the meaning of the militia clause suggests that, despite being voted a Super Lawyer, he is indeed an idiot. As a side note, his rant suggests that he doesn’t think too much of his clients either…

• Non sequitur. Prove to me that Ms. Creator exists. Of course, I can’t prove that she doesn’t. i also can’t prove that pixies don’t exist. But I tend to believe that supernatural beings are a figment of people’s hopes and imagination. I prefer to believe that my right to carry a weapon for self protection comes from common sense, common law, and my right to life (self preservation), as long as I do it responsibly. And if by “creator” you mean my parents, yes, they would support my right to self-preservation. One thing is for certain, I sure as hell don’t care what some jack-weed liberal politician thinks about my “rights.”

• Or maybe he just has a really nice “automatic” pistol that he doesn’t want getting scratched up by the seatbelt buckle in his car, or maybe he was wearing a jacket and took it off because he knew he was going to be too warm inside Costco…

Of course, this is all assuming that the author got the details correct and is being truthful.

43. Mr. Burdick appears to have a somewhat skewed point of view. He is a lawyer and a former prosecutor. I’ve seen many young people on the streets who appear to be sane well mannered even well dressed I’m even sure the neighbors of many a serial killer stated such things about people like Dahmer and the like. If you can tell a wise man solely by appearance then you need stand guard at the doors to the senate and stop the politicians from getting in.

44. Couple of problems with this guy’s story: 1. Costco does not seem to allow open carry in their stores so it is unlikely that the young man in the article was there. How would he have made it past the guy at the front that checks your Costco card when you enter ? 2. IF there was actually someone like the author says walking around in Costco how is the author able to tell so much about him by just looking at him ? The statements he makes about the young man with the gun reek of ego and an elitist attitude. More likely that the author made the whole thing up because his editor needed some anti-gun propaganda.

45. Criminal defense lawyer and health care cases. So, Mr. Burdick, is one of those lawyers who work so hard to make sure all the real criminals get back on the street instead of going to jail. Maybe he is so afraid because he knows how many creeps he has let out to live among us. Wonder if one of his favorite defenses is “Your Honor if my client just had not had such easy access to guns he would not be here today.” Blame the gun but never blame the guy who pulled the trigger as he is just a victim too. Another liberal lawyer who is responsible for much of the violent crime in our society today.

46. I’m calling BS on this. Costco bans guns in their stores and they do tell people who are open carrying that they need to disarm before entering. I think this guy is lying through his teeth. Pics or it didn’t happen.

47. When I’m out shopping, I legally carry – concealed. No one needs to know I’m armed. Without that component, this is a non story.

48. “jumps his grill”? Sounds like Burdick is trying to be the next Mickey Spillane. He’s even got the been-there-done-that tough guy picture the dames can’t resist.

I can see it now, coming in Fall 2015, “Open Carry Casket” by Jimmy Burdick.

49. It’s hard to believe that anyone with a name that sounds like “Bird Dick” would dare to discuss anything of a penile nature.

• It doesn’t matter. James has a burr up his dick (it says so right in the name) and thus, nothing else matters.

50. What a maroon…and I had a pleasant conversation with a similarly young guy open carrying (over the border in Indiana).And it was NO big deal. No training needed in Indiana either-so where are the bloodbaths?

51. I would say people with dreadlocks, tattoos, and shirts reading “BULLSHIRT” on them also give him the vapors and ruin HIS favorite Costco. But then I’d be making leaping assumptions about someone who I have never met.

52. Oh, I’m sure this Burdick guy will come around and straighten us all out. Maybe he can pistol whip us, or knock a few of our teeth down our throats, since he’s a real tough guy and all that. /rolleyes

53. Everyone should call his office at 248-335-5000 and tell him what they think of his article.

54. With his knowledge of the law and his comprehension level of the English language, I’m sure he has far more criminal defense clients in prison than those that he ever successfully prosecuted. I’m curious where one can buy those mind reading pills that he uses to acquire instant omniscient power and the ability to perceive a person’s thoughts, motives and past experiences.

• I am sure Mr. Former Prosecutor had many PCP users all up in his grill. Given his physic powers he should have had a 100% conviction rate.

I think the (possibly made up) 25 year old kid was a big time operator who could off him with his little finger. The gat is just a fashion statement because all the cool TV cops used them.

I give the kid with the gun a big edge in a fight with the tough talking former government employee. I also note that he didn’t say shit to him. Come on hoplophobe, call him out.

55. Lets all give three cheers for this gentleman’s newly discovered ESP!
I think we should all ask him, since: “I can just tell he truly has no idea what he’s doing” but, “since I just can tell”, and yet he’s only “pretty sure”, how is he now going to use this gift of precognition to benefit mankind. I’ll bet he has no intention of “just knowing” how to straighten out the mess we have made of the world in the last decade.
That’s the problem, and also the big reason for the mess we have made, people who BELIEVE they “just know” when in actuality they haven’t a clue…

56. I like how it’s really important that this guy he described was 25(ish).

Maybe this guy has never seen the Infantry, but below Staff Sergeant, they’re all just a bunch of kids. The look like they’re in their teens, barely their 20s. They’re trusted with things a bit more potent than a handgun on a regular basis.

Half of them look like dweebs (because half of teenage boys look like dweebs, I was among them) and might have been confused with MI if not for the patches on their shoulders.

This guy has no idea how to tell if someone is trained. Apparently you have to fulfill the “alpha male” stereotype to carry a sidearm and, apparently, to face down gangbangers, because the alpha male blueprint that other species adhere to isn’t now totally obsolete in humans or anything. I would think that he has the gun because he _doesn’t_ want to get into a fight, but that’s just me.

But, please, Mr. Burdick, allow your money to enlighten us all.

57. Death by Costco.
Mr. Burdick could do what the Las Vegas Costco manager did in 2010 when he got glimpse of West Point graduate Erik Scott’s .45. Tell him that Costco has an unwritten and un-posted policy banning persons who are carrying a firearm legally but tell him to kept it covered until he left. Problem is an overly aggressive “stock-boy” called the police and exaggerate the threat poised by Erik Scott describing him as acting wild and erratic. The police then sent multiple police cars and start evacuating the store. Then when Erik Scott exited, you could have a police officer shout three or four conflicting commands in five seconds, then fire seven shots at him, two of which actually hit him, killing him instantly. Oh, all you would have to do is check the video to see what happened, right? It seems that Rose Mary Woods was in charge of the video because there was a gap on the video that corresponded with this homicide.

It seems as if your trip to Costco better be in level IIIa body armor, because police killed another person at Costco in Sterling, VA in 2013 and this one wasn’t even carrying firearm conceal or open, but again acting “erratically”, Mhai Scott had been handing out free pizza samples, decided to leave. Since she was acting erratically and was agitated and was “armed with scissors” when Tazing her didn’t work, the police, as in Vegas, shot her down.

I always thought is was strange that Costco sold caskets, now I know why they do. “Death by Costco” is real if you are legally exercising your Constitutional right to carry a firearm and don’t know about some unwritten policy that is also un-posted. But maybe that only applies to Las Vegas, who knows. In the case of the pizza sampler, I would be agitated too of I stood there all day and everyone with a body mass index of over 25% fat was wolfing down pizza off of my tray.

I think we should appoint Mr. Burdick as the arms inspector for all Costcos and if he see someone, anyone whom is either carrying a firearm or he thinks may be carrying a firearm, concealed or openly, let’s give him the authority to just shoot them on sight as I don’t to take any chances. The fact that some people may be victims of stalkers, witnesses in court who have been targeted, or have been the object of an attempted hit is of no consequence. If Mr. Burdick is offended or suspects something is amiss, shoot them down and ask questions later. Give them15% off a casket. Better yet, if we can shut down the TSA, let’s hire the 25% that are sex perverts and have them operate 3D X-Rays and full body pat–downs at the front of Costco. Maybe then these punks with their cheap Rossi’s and Uncle Mike’s holsters will stop coming in. I mean, who do these peons think they are, citizens entitles to all the right and privileges of us, the better class?

58. I forgot to mention, when I sat as a circuit judge for 18 years, I always hated it when my prosecutor didn’t keep up with the relevant case law. If I had time to read the latest case law, then he did too, was always my thought. While seven years is getting kind of old now, I think if Mr. Burdick would read District of Columbia v. Heller, 554 U.S. 570 (2008) and McDonald, et al., v. City Of Chicago, Illinois, et al. 130 S.Ct. 3020 (2010) and spend a day and a half with Alan Gura like I did last year, he would not be as confused as to the current state of 2nd Amendment Law as he is.

59. “I ask, Sir, what is the militia? It is the whole people. To disarm the people is the best and most effectual way to enslave them.”
George Mason – Co-author of the Second Amendment during Virginia’s Convention to Ratify the Constitution, 1788


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$productListUser =$this->em->getRepository(ProductAdmin::class) ->findProductsUser(... Than public function findProductsUser(UserInterface $user, int$number) :?array { $listProductUser =$this->em->getRepository(ProductAdmin::class)->findBy(... seems to me that findProductsUser is method of ...

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Your code is mostly all right, especially given it's your first code attempt. I would say there is only on critical flaw. A post or a category is not a database connection. Hence it should be never extended from it. It would be like if you extend a human from a car simply because a human is going to ride a car. A car is a service used by a human, that ...

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You could exploit Laravel collections to achieve what you need. Most of your code is checking for the presence/absence of props on your arrays. Laravel internally exposes and uses the Illuminate\Support\Arr class that contains a lot of useful methods to work with arrays without the hassles of checking for key existance. It also allows you to use dot ...

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The code you posted doesn't seem to be doing what it says. From the way it is called and from the method's name one could tell it is intended to check if the id exists or not. But it doesn't return any answer to this question. instead it inserts some info into a database, which is extremely confusing. Also this code does some strange things like echoing the ...

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Function modelExist should check if model exists and return boolean. Your function does something completely different. It only needs that check for its job. public function modelExists(int $modelId): bool; To check existence of a row, you don't need all its columns. Select just 1 (literally) and check if you have received a row from the query or not. ... 0 You might want to decompose it into smaller pieces that will be easier to follow and eventually modify. You could also learn a bit about dependency injection. Creating new instances all around anytime you need them is not very good. Here is a very simple rewrite of your code and a lot of pieces are missing but I hope it gives some general guideline. It ... 1 The way you currently doing it would require all the websites to be written manually. A possible alternative would be to implement recursion (loops). The for loop: For loops are a good way of repeating a section of code/similar code a number of times. The number of times to repeat this code can be known explicitly, or you can determine it through a simple ... -1 you can simply use the for loop for such things,$totalUrl = 16;// change this number as your requirement for($i=0;$<$totalUrl;$i++){ $url =$chemin.'include/aaa/url.'$i'.php?param='.$param.'&page='.$p; // and here your code -include this or do whatever you want } 4 Dont call private methods in constructor, put the code into the constructor directly (well unless you have reason to call the same piece of code from elsewhere too, not your case tho). Don't put your db credentials into the class's constants. This way you are unable to use the class to connect to any other database. Well you can change their values, but ... 0 in addition to what has already been said, I'd suggest not using clientExists at all. just have a UNIQUE constraint on clientName, siteName and let the database enforce this for you. the reason is that your current code is both doing more work than is needed (the check for existence) as well not enough (the gap between the existence check and inserting a ... 1 Naming class Rosa tells me nothing. The name should scream out that it is a dependency injection container. PSR There is a standard interface for DI containers. https://github.com/php-fig/container/blob/master/src/ContainerInterface.php You might want to have you container implement it. Exit vs. Exception Implementing the PSR interface would ... 3 Reinventing the wheel You didnt make any indication that you are doing this as excercise. In that case you should try something already written and tested. Like Slim framework (http://www.slimframework.com/docs/v3/objects/router.html) which looks very similar to the "Express way". Also check out PSR interfaces. In case this is just an excercise for you or ... 1 I am going to post my thoughts without using profanity or defame thousands of developers that I've never met. I hope this will not lessen the perceived value or correctness of this content. First things first, I think it is important to know all of the viable tools at your disposal with php. Yes, str_replace() and preg_replace() are the two widely used ... 2 Toward optimization and better functionality consider using short array syntax [] instead of old-fashioned array() do not designate redundant captured groups such as ([0-9]{2})...([0-9]{2}) if you only need the 1st captured group ([^`]*?) regex [0-9] has a concise equivalent for designating digits - \d All those preg_replace calls in the initial approach ... 4 Most of such advises are crystal clear bullshit, on so many levels. You need to understand that such recommendations are never a result of some quality research, but just a rephrase of some vague rumor. The internet is full of chimpanzees. This particular advise didn't make any sense even for PHP5. That said, a set of consequent function calls apparently ... 2 SQL injection should not be a problem, as long as you pass any user input to queries through placeholders, which you do. I have a few other remarks though Single Responsibility Principle In the first code snippet you do too much things. You decode request json, you talk to db. you handle the logic, you maintain response structure. It would be wise to ... 2 Ad 1) it Is ok to pass id in the Array data of you want to change the id. If you were asking if you can omit the id argument. Then yes but you Will never be able to change id And honestly it becomes more verbose to use. And honestly it Is quite premature to expect this on this generic level. Ad 2) if "wrong" means empty id or database unreachable and ... 0 In a sutuation when a block of code is present in both branches of an if statement, you can move this common part out of this statement. for example, if (some condition) {$a = $x;$b = $y;$a = $z; } else {$a = $x;$b = $y;$a = null; } it can be rewritten to $a =$x; $b =$y; if (some condition) { $a =$z; } else { \$a = ...

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text:
## Algebra 1

$\approx$14.2ft
The golden ratio is $\frac{1+\sqrt{5}}{2}=\frac{length}{width}$. If the length is 23 ft, we solve for $w$, or the width. We can do this by cross multiplying. $\frac{1+\sqrt{5}}{2}=\frac{23}{w} w(1+\sqrt{5})=46, w=\frac{46}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}=\frac{46-46\sqrt{5}}{1-5}=\frac{46-46\sqrt{5}}{-4}=\frac{23\sqrt{5}-23}{2} \approx 14.2ft$