Consider the (5,k)-SAT problem: Input: A boolean formula in CNF form such that there are at most five literals in each clause, and an integer k ≥ 1.Output: An assignment of variables such that exactly k clauses are unsatisfied, or return NO if such an assignment does not exist. Prove that (5,k)-SAT is NP-complete.

Let y_t=(y_(t-τ),…,y_(t-1)) be a vector of preceding spike counts up to but not including time t Let x_t=(x_(t-τ),…,x_(t-1)) represent the vector of preceding stimuli up to but not including time t. To mimic the refractory period in the GLM, if a spike occurs just prior to time t, the convolution of the spike occurrence with the post-spike filter h 

For each of the following structures, define the lesion and determine whether it has any effect on shoulder instability; why or why not? a. Hill-Sachs. defect/lesion b. Bankart lesion c. SLAP tears

Answer the question based on the scenario presented: History: A 25-year-old male student at NAU presents with shoulder pain and a feeling of instability after a dislocation while playing on NAU’s club rugby. He reports recurrent episodes of the shoulder “slipping out” since the initial injury. Signs and Symptoms: Pain with shoulder abduction and external rotation Tenderness over the anterior shoulder Weakness in shoulder external rotation Question: What is the most likely diagnosis, and what two (2) special tests would you use to confirm your diagnosis?

A Hill-Sachs lesion occurs where on the humeral head, specific to the articular cartilage? 

Which of the follow structures is NOT affected by the injury of impingement?

What test would you select to confirm a subacromial impingement diagnosis?

A positive Yergason’s test indicates what pathology?

Use the scenario to answer the following question: Background: A 50-year-old female presents with shoulder stiffness and pain, particularly in the morning. She has a history of diabetes and reports that the pain has been gradually worsening over the past six months. She describes the pain as dull and aching, with occasional sharp pains during certain movements. She has difficulty with daily activities such as dressing and reaching overhead. Question: What is the most likely diagnosis?

Use this scenario to answer the next few questions: A 35-year-old male presents with shoulder pain after a fall while playing basketball. He reports pain on the lateral aspect of the shoulder, difficulty lifting his arm, and a feeling of instability. On examination, there is tenderness over the acromioclavicular (AC) joint, limited range of motion, and weakness in abduction.   What special test would you perform to assess the integrity of the AC joint?