BACKGROUND:In the prehospital tranexamic acid (TXA) for traumatic brain injury (TBI) trial, TXA administered within 2 hours of injury in the out-of-hospital setting did not reduce mortality in all patients with moderate/severe traumatic brain injury (TBI). We examined the association between TXA dosing arms, neurologic outcome, and mortality in patients with intracranial hemorrhage (ICH) on computed tomography (CT). METHODS:This was a secondary analysis of the Prehospital Tranexamic Acid for TBI Trial ( ClinicalTrials.gov [NCT01990768]) that randomized adults with moderate/severe TBI (Glasgow Coma Scale score < 13) and systolic blood pressure ≥ 90 mm Hg within 2 hours of injury to a 2-g out-of-hospital TXA bolus followed by an in-hospital saline infusion, a 1-g out-of-hospital TXA bolus/1-g in-hospital TXA infusion, or an out-of-hospital saline bolus/in-hospital saline infusion (placebo). This analysis included the subgroup with ICH on initial CT. Primary outcomes included 28-day mortality, 6-month Glasgow Outcome Scale-Extended (GOSE) ≤ 4, and 6-month Disability Rating Scale (DRS). Outcomes were modeled using linear regression with robust standard errors. RESULTS:The primary trial included 966 patients. Among 541 participants with ICH, 28-day mortality was lower in the 2-g TXA bolus group (17%) compared with the other two groups (1-g bolus/1-g infusion 26%, placebo 27%). The estimated adjusted difference between the 2-g bolus and placebo groups was -8·5 percentage points (95% confidence interval [CI], -15.9 to -1.0) and between the 2-g bolus and 1-g bolus/1-g infusion groups was -10.2 percentage points (95% CI, -17.6 to -2.9). Disability Rating Scale at 6 months was lower in the 2-g TXA bolus group than the 1-g bolus/1-g infusion (estimated difference - 2.1 [95% CI, -4.2 to -0.02]) and placebo groups (-2.2 [95% CI, -4.3, -0.2]). Six-month GOSE did not differ among groups. CONCLUSION:A 2-g out-of-hospital TXA bolus in patients with moderate/severe TBI and ICH resulted in lower 28-day mortality and lower 6-month DRS than placebo and standard TXA dosing. LEVEL OF EVIDENCE:Therapeutic/Care Management; Level II.

The aim of this study was to understand the risk of developing attention-deficit/hyperactivity disorder (ADHD) or learning disability (LD) after childhood traumatic brain injury (TBI) in a population-based birth cohort. Cases of TBI for children from birth to 10 years were confirmed and stratified by severity of injury. For each TBI case, two age-matched and sex-matched referents without TBI were identified from the same birth cohort. Presence of ADHD and LD before age 19 were confirmed using medical and/or school records. Associations between TBI exposure and subsequent ADHD or LD were assessed in multivariable Cox regression models, adjusting for maternal age, education, and race. The incidence rate of TBI before age 10 was 1,156 per 100,000 person-years. Children who had a TBI before age 10 were more likely to have met the research criteria for ADHD (hazard ratio [HR], 1.68; 95% CI, 1.15-2.45) or LD (HR, 1.29; 95% CI, 1.00-1.68) by age 19. No statistically significant associations were shown between TBI and ADHD or LD when restricted to definite and probable TBI cases (consistent with moderate to severe and mild TBI, respectively) and their referents. Significant associations were shown when the analysis was confined to possible TBI cases (consistent with concussive TBI) and their referents (ADHD: HR, 2.05; 95% CI, 1.31-3.20; and LD: HR, 1.42; 95% CI, 1.05-1.91). Increased risk for developing ADHD and LD by adulthood was shown particularly for children with the least-severe injuries, indicating that factors other than trauma-related altered brain function likely contribute to this risk.

A graph where each vertex v has a list L(v) of available colors is L-colorable if there is a proper coloring such that the color of v is in L(v) for each v. A graph is k-choosable if every assignment L of at least k colors to each vertex guarantees an L-coloring. Given a list assignment L, an L-request for a vertex v is a color c is an element of L(v). In this paper, we look at a variant of the widely studied class of precoloring extension problems from Dvorak, Norin, and Postle (J. Graph Theory, 2019), wherein one must satisfy "enough'', as opposed to all, of the requested set of precolors. A graph G is epsilon-flexible for list size k if for any k-list assignment L, and any set S of L-requests, there is an L-coloring of G satisfying epsilon-fraction of the requests in S. It is conjectured that planar graphs are epsilon-flexible for list size 5, yet it is proved only for list size 6 and for certain subclasses of planar graphs. We give a stronger version of the main tool used in the proofs of the aforementioned results. By doing so, we improve upon a result by Masarik and show that planar graphs without K-4(-) are epsilon-flexible for list size 5. We also prove that planar graphs without 4-cycles and 3-cycle distance at least 2 are epsilon-flexible for list size 4. Finally, we introduce a new (slightly weaker) form of epsilon-flexibility where each vertex has exactly one request. In that setting, we provide a stronger tool and we demonstrate its usefulness to further extend the class of graphs that are epsilon-flexible for list size 5. (C) 2021 The Author(s). Published by Elsevier B.V.

Background: Injured patients have early changes to normal coagulation that can impact long term risk for thrombotic complications. There is little known about how age impacts biomarkers of coagulation after traumatic injury. In this pilot study, we aimed to characterize thrombin generation kinetics, a known predictor of venous thromboembolism, in trauma patients across the age spectrum.Methods: Citrated plasma samples were collected from 174 trauma patients (3-94 years old). Thrombin generation kinetics were measured using calibrated automated thrombogram (CAT) and expressed as lag time (LT - minutes) and time to peak (ttPeak - minutes). Kruskal-Wallis, Spearman correlation, and multivariable regression analysis were carried out. Data in median and quartiles [Q1, Q3]. P < 0.05 significant.Results: Pediatric patients (n = 14) had shortest LT and ttPeak compared to adult and geriatric (n = 43), who had longest (LT: 2.67 [2.48, 3.00] vs. 2.93 [2.56, 3.48] vs. 3.15 [2.74, 3.67], p = 0.029; ttPeak: 4.98 [4.67, 5.67] vs. 5.53 [5.00, 6.56] vs. 5.94 [5.52, 6.91], p = 0.011). LT and ttPeak correlated with age (Spearman 0.285 and 0.305, both p < 0.001). Clinical factors, specifically, age, injury severity score, and transfusion status were associated with LT and ttPeak in multivariable models.Conclusions: Trauma patients exhibit prolonged initiation and time to peak thrombin generation with age. Further studies are needed to determine the age-specific role of thrombin generation kinetics in thrombotic complications after trauma.

Activation of the fibrinolytic system plays a central role in the host response to trauma. There is significant heterogeneity in the degree of fibrinolysis activation at baseline that is usually assessed by whole blood thromboelastography (TEG). Few studies have focused on plasma markers of fibrinolysis that could add novel insights into the frequency and mechanisms of fibrinolytic activation in trauma. Global fibrinolysis in plasma was assessed using a modified euglobulin clot lysis time (ECLT) assay in 171 major trauma patients and compared to commonly assessed analytes of fibrinolysis. The median ECLT in trauma patients was significantly shorter at 8.5 h (IQR, 1.3-19.5) compared to 19.9 h (9.8-22.6) in healthy controls (p < 0.0001). ECLT values ≤2.5th percentile of the reference range were present in 83 (48.5%) of trauma patients, suggesting increased fibrinolytic activation. Shortened ECLT values were associated with elevated plasmin-antiplasmin (PAP) complexes and free tissue plasminogen activator (tPA) levels in plasma. Sixteen (9.2%) individuals met the primary outcome for massive transfusion, here defined as the critical administration threshold (CAT) of 3 units of packed red cells in any 60-minute period within the first 24 h. In a univariate screen, plasma biomarkers associated with CAT included D-dimer (p < 0.001), PAP (p < 0.05), free tPA (p < 0.05) and ECLT (p < 0.05). We conclude that fibrinolytic activation, measured by ECLT, is present in a high proportion of trauma patients at presentation. The shortened ECLT is partially driven by high tPA levels and is associated with high levels of circulating PAP complexes. Further studies are needed to determine whether ECLT is an independent predictor of trauma outcomes.

Introduction Plasma thrombin generation kinetics as measured by the calibrated automated thrombogram (CAT) assay is a predictor of symptomatic venous thromboembolism after trauma. We hypothesized that data from a new prototype assay for measurement of thrombin generation kinetics in fresh whole blood (near patient testing of thrombin generation), will correlate with the standard CAT assay in the same patients, making it a potential tool in the future care of trauma patients. Methods Patients were enrolled from June 2018 to February 2020. Within 12 hours of injury, blood samples were collected simultaneously for both assays. Variables compared and correlated between assays were lag time, peak height, time to peak, and endogenous thrombin potential. Data are presented as median with interquartile range (IQR). Spearman and Pearson correlations were estimated and tested between both assays; a P value of <0.05 was considered to be significant. Results A total of 64 trauma patients had samples analyzed: injury severity score = 17 (IQR), 10-26], hospital length of stay = 7.5 (IQR), 2-18) days, age = 52 (IQR, 35-63) years, 71.9% male, and 42.2% of patients received a transfusion within 24 hours of injury. Thrombin generation parameters between plasma and whole blood were compared and found that all parameters of the two assays correlate in trauma patients. Conclusion In this pilot study, we have found that a novel point-of-care whole blood thrombin generation assay yields results with modest but statistically significant correlations to those of a standard plasma thrombin generation assay. This finding supports studying this device in a larger, adequately powered study.

In 1984, Matthews and Sumner conjectured that every 4-connected, claw-free graph contains a Hamiltonian cycle. This still unresolved conjecture has been the motivation for research into the existence of other cycle structures. In this paper, we consider the stronger property of pancyclicity for 4-connected graphs. In particular, we show that every 4-connected, { K 1 , 3 , N ( i , j , k ) }-free graph, where i , j , k ≥ 1 and i + j + k = 6, is pancyclic. This, together with results by Ferrara, Morris, Wenger, and Ferrara et al. completes a characterization of the graphs Y such that every { K 1 , 3 , Y }-free graph is pancyclic. In addition, this represents the best known progress towards answering a question of Gould concerning a characterization of the pairs of forbidden subgraphs that imply pancyclicity in 4-connected graphs.

Tension pneumothorax is a life-threatening condition that can develop when either the visceral pleura is disrupted, or with injury to the tracheobronchial tree. Rapid, accurate diagnosis and appropriate management are required to prevent significant atelectasis, hypoxia, circulatory arrest, and ultimate patient demise. Needle decompression is the current standard of care for the management of tension pneumothorax. Healthcare providers struggle to assess the success of decompression due to a lack of any immediate objective feedback. The gaseous composition of tension pneumothorax is similar to that of end respiratory gas. This includes an increased partial pressure of carbon dioxide in comparison to atmospheric air, which makes colorimetric capnography an ideal confirmatory test. This colorimetric capnography device may help the healthcare providers to make an objective and accurate assessment of the success of the needle decompression, in particular in prehospital environments.

We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's spontaneous additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses during clinical, task-based interviews. All participants spontaneously used one of three additive strategies—counting-on, doubling, or break-apart-make-ten (BAMT)—to correctly solve an addition word problem (8 + 7). We found between-group differences, with asymmetric association of those ordinal variables. We found counting-on to be mainly related to premultiplicative reasoning and BAMT to mDC reasoning. We discuss the theoretical significance and implications of this corroboration of Steffe's model.

Let $\mathcal{C}$ be a family of edge-colored graphs. A $t$-edge colored graph $G$ is $(\mathcal{C}, t)$-saturated if $G$ does not contain any graph in $\mathcal{C}$ but the addition of any edge in any color in $[t]$ creates a copy of some graph in $\mathcal{C}$. Similarly to classical saturation functions, define $\mathrm{sat}_t(n, \mathcal{C})$ to be the minimum number of edges in a $(\mathcal{C},t)$ saturated graph. Let $\mathcal{C}_r(H)$ be the family consisting of every edge-colored copy of $H$ which uses exactly $r$ colors. In this paper we consider a variety of colored saturation problems. We determine the order of magnitude for $\mathrm{sat}_t(n, \mathcal{C}_r(K_k))$ for all $r$, showing a sharp change in behavior when $r\geq \binom{k-1}{2}+2$. A particular case of this theorem proves a conjecture of Barrus, Ferrara, Vandenbussche, and Wenger. We determine $\mathrm{sat}_t(n, \mathcal{C}_2(K_3))$ exactly and determine the extremal graphs. Additionally, we document some interesting irregularities in the colored saturation function.

INTRODUCTION We hypothesize that a patient (pt) with accelerated thrombin generation, time to peak height (ttPeak), will have a greater odds of meeting critical administration threshold (CAT) criteria (> 3 packed red blood cell [pRBC] transfusions [Tx] per 60 minute interval), within the first 24 hours after injury, independent of international normalized ratio (INR). METHODS In a prospective cohort study, trauma patients were enrolled over a 4.5 year period and serial blood samples collected at various time points. We retrospectively stratified pts into 3 categories: 1) CAT+ 2) CAT- but receiving some pRBC Tx 3) receiving no Tx within the first 24 hours. Blood collected prior to Tx was analyzed for thrombin generation parameters and PT/INR. RESULTS Total of 484 trauma pts were analyzed: Injury severity score = 13 [7,22], age = 48 [28, 64] years, and 73% male. Fifty pts met criteria for CAT+, 64 pts CAT-, and 370 received no Tx. Risk factors for meeting CAT+: decreased arrival systolic blood pressure (OR 2.82 [2.17, 3.67]), increased INR (OR 2.09, [1.66, 2.62]) and decreased time to peak OR 2.27 [1.74, 2.95]). These variables remained independently associated with increased risk of requiring Tx in a multivariable logistic model, after adjusting for sex and trauma type. CONCLUSIONS Pts in hemorrhagic shock, who meet CAT+ criteria, are characterized by accelerated thrombin generation. In our multivariable analysis, both ttPeak and PT/INR have a complementary role in predicting those injured patients who will require a high rate of Tx.

Bootstrap percolation is a deterministic cellular automaton in which vertices of a graph G begin in one of two states, "dormant" or "active." Given a fixed positive integer r, a dormant vertex becomes active if at any stage it has at least r active neighbors, and it remains active for the duration of the process. Given an initial set of active vertices A, we say that G r-percolates (from A) if every vertex in G becomes active after some number of steps. Let m(G,r) denote the minimum size of a set A such that G r-percolates from A. Bootstrap percolation has been studied in a number of settings and has applications to both statistical physics and discrete epidemiology. Here, we are concerned with degree-based density conditions that ensure m(G,2)=2. In particular, we give an Ore-type degree sum result that states that if a graph G satisfies sigma 2(G)>= n-2, then either m(G,2)=2 or G is in one of a small number of classes of exceptional graphs. (Here, sigma 2(G) is the minimum sum of degrees of two nonadjacent vertices in G.) We also give a Chvatal-type degree condition: If G is a graph with degree sequence d1 <= d2 <= MIDLINE HORIZONTAL ELLIPSIS <= dn such that di >= i+1 or dn-i >= n-i-1 for all 1 <= i

A growing part of the efforts to promote student engagement and success in undergraduate STEM are the family of Student Support and Outreach Programs (SSOPs), which task undergraduate students with providing support and mentoring to their peers and near-peers. Research has shown that these programs can provide a variety of benefits for the programs’ recipients, including increased academic achievement, satisfaction, retention, and entry into STEM careers. This paper extends this line of inquiry to investigate how participation in these programs impacts the undergraduate STEM students that provide the mentoring (defined here as undergraduate mentor-teachers or UMTs). We use activity theory to explore the nature of metacognition and identity development in UMTs engaged in two programs at a public urban-serving university in the western USA: a STEM Learning Assistant program and a program to organize middle and high school STEM clubs. Constructs of metacognition and identity development are seen as critical outcomes of experiential STEM inreach and outreach programs. Written reflections were collected throughout implementation of two experiential STEM inreach and outreach programs. A thematic analysis of the reflections revealed UMTs using metacognitive strategies including content reflection and reinforcement and goal setting for themselves and the students they were supporting. Participants also showed metacognitive awareness of the barriers and challenges related to their role in the program. In addition to these metacognitive processes, the UMTs developed their science identities by attaching different meanings to their role as a mentor in their respective programs and setting performance expectations for their roles. Performance expectations were contingent on pedagogical skills and the amount and type of content knowledge needed to effectively address student needs. The ability to meet students’ needs served to validate and verify UMTs’ role in the program, and ultimately their own science identities. Findings from this study suggest that metacognitive and identity developments are outcomes shaped not only by undergraduate students’ experiences, but also by their perceptions of what it means to learn and teach STEM. Experiential STEM inreach and outreach programs with structured opportunities for guided and open reflections can contribute to building participants’ metacognition and enhancing their science identities.

Tension pneumothorax is a common cause of mortality in trauma. Tension pneumothorax is the confinement of respired gases within the pleural cavity at increasing pressure resulting in hemodynamic collapse. Decompression is crucial in management. Emergency needle thoracostomy is a life-saving maneuver that allows atmospheric pressure equilibration and partial restoration of cardiac filling. Needle decompressions are usually performed under noisy, tense, and stressful circumstances, and objective assessment of success is difficult in the field. A device which is simple that objectively informs operators of successful decompression would be clinically useful. In previous work, we have demonstrated end-expiratory gas and gaseous composition of tension pneumothorax are similar due to increased carbon dioxide partial pressure relative to atmospheric gas composition. Therefore, a simple solution to objective needle decompression may be colorimetric capnography.We report a case of 58-year-old male treated by EMS following a motorcycle accident with left-sided chest pain, hypoxia, hypotension, and clinical findings of tension pneumothorax. Needle decompression with colorimetric capnography using the device indicated decompression of his tension pneumothorax, with appropriate temporizing success.

CONTEXT:Interscholastic heat policies for football have not been evidence based. Therefore, their effectiveness in mitigating exertional heat illness has not been assessed. OBJECTIVE:To discuss the development of the Georgia High School Association heat policy and assess the effectiveness of revised guidelines. DESIGN:Descriptive epidemiology study. SETTING:Georgia high schools. PATIENTS OR OTHER PARTICIPANTS:Interscholastic football players in grades 9 through 12. MAIN OUTCOME MEASURE(S):Heat syncope and heat exhaustion (HS/HE) illness rates (IRs) were calculated per 1000 athlete-exposures (AEs), and relative risk (RR) was calculated as a ratio of postpolicy (POST) IR divided by prepolicy (PRE) IR. RESULTS:A total of 214 HS/HE cases (172 PRE, 42 POST) and 341 348 AEs (178 230 PRE, 163 118 POST) were identified. During the first 5 days of the PRE period, approximately 50% of HS/HE illnesses occurred; HS/HE IRs doubled when practice sessions increased from 2 to 2.5 hours and tripled for practices ≥3 hours. The HS/HE IRs in the PRE period increased from 0.44/1000 AEs for wet-bulb globe temperatures (WBGTs) of <82°F (<27.8°C) to >2.0/1000 AEs for WBGTs from 87°F (30.6°C) to 89.9°F (32.2°C). The RRs comparing PRE and POST policy periods were 0.29 for WBGTs of <82.0°F (<27.80°C), 0.65 for WBGTs from 82.0°F (27.8°C) to 86.9°F (30.5°C), and 0.23 for WBGTs from 87.0°F (30.6°C) to 89.9°F (32.2°C). No HS/HE illnesses occurred in the POST period for WBGTs at >90°F (>32.3°C). CONCLUSIONS:Results from the PRE period guided the Georgia High School Association to revise its heat and humidity policy to include a mandated 5-day acclimatization period when no practices may exceed 2 hours and the use of WBGT-based activity-modification categories. The new policy reduced HS/HE IRs by 35% to 100%, depending on the WBGT category. Our results may be generalizable to other states with hot and humid climates similar to that of Georgia.

Importance Traumatic brain injury (TBI) is the leading cause of death and disability due to trauma. Early administration of tranexamic acid may benefit patients with TBI. Objective To determine whether tranexamic acid treatment initiated in the out-of-hospital setting within 2 hours of injury improves neurologic outcome in patients with moderate or severe TBI. Design, Setting, and Participants Multicenter, double-blinded, randomized clinical trial at 20 trauma centers and 39 emergency medical services agencies in the US and Canada from May 2015 to November 2017. Eligible participants (N = 1280) included out-of-hospital patients with TBI aged 15 years or older with Glasgow Coma Scale score of 12 or less and systolic blood pressure of 90 mm Hg or higher. Interventions Three interventions were evaluated, with treatment initiated within 2 hours of TBI: out-of-hospital tranexamic acid (1 g) bolus and in-hospital tranexamic acid (1 g) 8-hour infusion (bolus maintenance group; n = 312), out-of-hospital tranexamic acid (2 g) bolus and in-hospital placebo 8-hour infusion (bolus only group; n = 345), and out-of-hospital placebo bolus and in-hospital placebo 8-hour infusion (placebo group; n = 309). Main Outcomes and Measures The primary outcome was favorable neurologic function at 6 months (Glasgow Outcome Scale-Extended score >4 [moderate disability or good recovery]) in the combined tranexamic acid group vs the placebo group. Asymmetric significance thresholds were set at 0.1 for benefit and 0.025 for harm. There were 18 secondary end points, of which 5 are reported in this article: 28-day mortality, 6-month Disability Rating Scale score (range, 0 [no disability] to 30 [death]), progression of intracranial hemorrhage, incidence of seizures, and incidence of thromboembolic events. Results Among 1063 participants, a study drug was not administered to 96 randomized participants and 1 participant was excluded, resulting in 966 participants in the analysis population (mean age, 42 years; 255 [74%] male participants; mean Glasgow Coma Scale score, 8). Of these participants, 819 (84.8%) were available for primary outcome analysis at 6-month follow-up. The primary outcome occurred in 65% of patients in the tranexamic acid groups vs 62% in the placebo group (difference, 3.5%; [90% 1-sided confidence limit for benefit, -0.9%]; P = .16; [97.5% 1-sided confidence limit for harm, 10.2%]; P = .84). There was no statistically significant difference in 28-day mortality between the tranexamic acid groups vs the placebo group (14% vs 17%; difference, -2.9% [95% CI, -7.9% to 2.1%]; P = .26), 6-month Disability Rating Scale score (6.8 vs 7.6; difference, -0.9 [95% CI, -2.5 to 0.7]; P = .29), or progression of intracranial hemorrhage (16% vs 20%; difference, -5.4% [95% CI, -12.8% to 2.1%]; P = .16). Conclusions and Relevance Among patients with moderate to severe TBI, out-of-hospital tranexamic acid administration within 2 hours of injury compared with placebo did not significantly improve 6-month neurologic outcome as measured by the Glasgow Outcome Scale-Extended. This randomized clinical trial compares the effects of an out-of-hospital tranexamic acid bolus vs placebo within 2 hours of traumatic brain injury (TBI) on 6-month functional neurologic outcome (Glasgow Coma Scale-Extended score >4) in patients with moderate or severe TBI. Question Does early administration of tranexamic acid to patients with moderate or severe traumatic brain injury improve neurologic outcome at 6 months? Findings In this randomized multicenter clinical trial that included 966 participants enrolled in the out-of-hospital setting by paramedics, treatment with tranexamic acid as an out-of-hospital bolus with or without in-hospital infusion, compared with placebo as an out-of-hospital bolus and in-hospital infusion, resulted in a favorable neurologic outcome (defined as Glasgow Outcome Scale-Extended score >4) in 65% vs 62% of patients at 6 months, a difference that was not statistically significant. Meaning Among participants suspected of having moderate or severe traumatic brain injury, out-of-hospital administration of tranexamic acid compared with placebo did not significantly improve 6-month neurologic recovery.

The 2012 National Institutes of Health (NIH) Biomedical Workforce Working Group Report documented that graduate training in the biomedical sciences predominantly prepares people for academic research positions. The report recommended that NIH provide funds for institutions to develop broader career development opportunities, including training related to teaching. Indeed, teaching is not only a required component of any faculty position, it is the primary task for trainees who seek employment at small liberal arts colleges and other primarily undergraduate institutions. NIH funding for the BEST (Broadening Experiences in Scientific Training) programs allowed us to develop a six-week training workshop for bioscience trainees to introduce participants to research-based, student-centered pedagogies and instructional design techniques and to inspire them to view teaching as an intellectual endeavor. The methods and outcomes of our case study should be applicable in a variety of programs and organizations, especially those with a separate health science campus, where faculty mentors often do not teach many classes and there are few, if any, apprenticeship-teaching opportunities for trainees.

The distinguishing number of a graph G, denoted D(G), is the minimum number of colors needed to produce a coloring of the vertices of G so that every nontrivial automorphism interchanges vertices of different colors. A list assignment L on a graph G is a function that assigns each vertex of G a set of colors. An L-coloring of G is a coloring in which each vertex is colored with a color from L(v). The list distinguishing number of G, denoted Dℓ(G) is the minimum k such that every list assignment L that assigns a list of size at least k to every vertex permits a distinguishing L-coloring. In this paper, we prove that when n is large enough, the distinguishing and list-distinguishing numbers of Kn□Km agree for almost all m>n, and otherwise differ by at most one. As a part of our proof, we give (to our knowledge) the first application of the Combinatorial Nullstellensatz to setting of distinguishing graph colorings and also prove an inequality for the binomial distribution that may be of independent interest.