• Male and Female patients aged 18-80 presenting for carotid endarterectomy
• Patients not felt suitable for carotid endarterectomy and those with impaired decision-making capacity

• Subjects with a PFO who have had an ischemic stroke within the last 547 days
• Atherosclerosis or other arteriopathy of the intracranial and extracranial vessels associated with a ≥ 50% lumen diameter supplying the involved lesion
• Intra-cardiac thrombus or tumor
• Documented evidence of venous thrombus in the vessels through which access to the PFO is gained
• Acute or recent (within 6 months prior to consent) myocardial infarction or unstable angina
• Left ventricular aneurysm or akinesis
• Mitral valve stenosis or severe mitral regurgitation requiring intervention irrespective of etiology
• Aortic valve stenosis (mean gradient >40 mmHg) or severe aortic valve regurgitation
• Mitral or aortic valve vegetation or prosthesis
• Aortic arch plaques protruding greater than 4mm into the aortic lumen
• Left ventricular dilated cardiomyopathy with depressed left ventricular ejection fraction (LVEF less than 35%)
• Subjects with other source of right to left shunts, including an atrial septal defect and/or fenestrated septum
• Chronic, persistent, or paroxysmal atrial fibrillation or atrial flutter
• Pregnancy at the time of implant
• Age less than 18 years or greater than 60 years at time of consent
• Active endocarditis or other untreated infections
• Organ failure (kidney, liver or lung) Kidney failure: Poor urine output of less than 1 cc/kg/hr with elevated BUN levels (above the normal reference range for the laboratory at the investigational site). Liver failure: Liver enzymes outside the normal reference range for the laboratory at the investigational site: poor liver function as assessed by elevated PT (above the normal reference range for the laboratory at the investigational site) and low total protein and albumin (below the normal reference range for the laboratory at the investigational site). Lung failure: Respiratory failure is retention of carbon dioxide more than 60 mmHg, poor oxygenation with oxygen tension less than 40 mmHg in room air or the need for assisted ventilation.
• Uncontrolled hypertension defined as sustained elevated systemic blood pressure to more than 160/90 mmHg with medications
• Uncontrolled diabetes defined as continued elevated glucose levels in spite of administration of insulin/levels of more than 200 mg with presence of glucose in the urine
• Diagnosis of lacunar infarct probably due to intrinsic small vessel as qualifying stroke event Definition: Ischemic stroke in the distribution of a single, small deep penetrating vessel in a patient with any of the following: 1) a history of hypertension (except in the first week post stroke); 2) history of diabetes mellitus; 3) Age >/= 50; or 4) MRI or CT shows leukoaraiosis greater than symmetric, well-defined periventricular caps or bands (European Task Force on Age-Related White Matter Changes rating scale score > 0)
• Arterial dissection as cause of stroke
• Subjects who test positive with one of the following hypercoagulable states; Anticardiolipin Ab of the IgG or IgM (≥30), Lupus anticoagulant, B2-glycoprotein-1 antibodies (≥30) or persistently elevated homocysteine (>20)
• Unable to take antiplatelet therapy
• Anatomy in which the AMPLATZERTM PFO Occluder device size required would interfere with intracardiac or intravascular structures such as valves or pulmonary veins
• Vasculature, through which access to the PFO is gained, is inadequate to accommodate the appropriate sheath size
• Malignancy or other illness where life expectancy is less than 2 years
• Subjects who will not be available for follow-up for the duration of the trial
• Inability to obtain Informed Consent from patient
• Index stroke of poor outcome (modified Rankin score greater than 3)

1. TIA with ABCD2 ≥4 or ischemic stroke, within the prior 14 days. 1. pre-event inability to perform all of own basic ADLs 2. unable to obtain informed consent from subject or legally authorized representative 3. incarcerated 4. known pregnancy 5. current mechanical ventilation (can enroll later if this resolves) or tracheostomy 6. current use of positive airway pressure, or use within one month prior to stroke 7. anatomical or dermatologic anomaly that makes use of CPAP interface unfeasible 8. severe bullous lung disease 9. history of prior spontaneous pneumothorax or current pneumothorax 10. hypotension requiring current treatment with pressors (can enroll later if this resolves) 11. other specific medical circumstances that conceivably, in the opinion of the site PI, could render the patient at risk of harm from use of CPAP 12. massive epistaxis or previous history of massive epistaxis 13. cranial surgery or head trauma within the past 6 months, with known or possible CSF leak or pneumocephalus 14. recent hemicraniectomy or suboccipital craniectomy (i.e. those whose bone has not yet been replaced), or any other recent bone removal procedure for relief of intracranial pressure 15. current receipt of oxygen supplementation >4 liters per minute 16. current contact, droplet, respiratory/airborne precautions

• Participants receiving health care through the Oneida Health Council Program
• Participants deemed to be at high risk for stroke by modified Framingham assessment of medical history, including cerebral cardiovascular symptomatology, hypertension, diabetes, smoking, BMI
• Willingness to participate in the study, including two-year follow-up
• Controls will be selected using the same criteria with the exception that upon screening, they are not deemed to be at high risk for stroke.
• Presence of established dementia
• Inability to participate in physical and exercise programs due to preexisting disability
• Illiteracy
• Prior carotid procedure altering ultrasound finding
• Presence of medical condition precluding participation or follow-up over a two-year period of time.

• Acute focal symptoms or signs of any duration associated with imaging, pathological, or other objective evidence of arterial infarction OR clinical evidence of cerebral, spinal cord, or retinal focal arterial ischemic injury based on symptoms persisting greater than or equal to 24 hours that occurred within 30 days prior to randomization
• Index stroke is attributed to 70-99% stenosis (or flow gap on MRA) of a major intracranial artery (carotid artery, middle cerebral artery (M1 or M2), vertebral artery (V4), basilar artery, posterior cerebral artery (P1), or anterior cerebral artery (A1)) documented by CTA, MRA, or catheter angiography
• Modified Rankin Scale score of ≤ 4, at time of consent
• Ability to swallow pills
• At least 30 years of age, inclusive, at time of consent
• Subjects 30-49 years of age are required to meet at least ONE of the following additional criteria below to qualify for the study: 1. diabetes treated with insulin for at least 15 years 2. at least 2 of the following atherosclerotic risk factors: hypertension (BP > 140/90 or on antihypertensive therapy); dyslipidemia (LDL > 130 mg /dl or HDL < 40 mg/dl or fasting triglycerides > 150 mg/dl or on lipid lowering therapy); smoking; non-insulin dependent diabetes or insulin dependent diabetes of less than 15 years duration; any of the following vascular events occurring in a parent or sibling who was < 55 years of age for men or < 65 years of age for women at the time of the event: myocardial infarction, coronary artery bypass, coronary angioplasty or stenting, stroke, carotid endarterectomy or stenting, peripheral vascular surgery for atherosclerotic disease 3. personal history of any of the following: myocardial infarction, coronary artery bypass, coronary angioplasty or stenting, carotid endarterectomy or stenting, or peripheral vascular surgery for atherosclerotic disease 4. any stenosis of an extracranial carotid or vertebral artery, another intracranial artery, subclavian artery, coronary artery, iliac or femoral artery, other lower or upper extremity artery, mesenteric artery, or renal artery that was documented by non-invasive vascular imaging or catheter angiography and is considered atherosclerotic 5. aortic arch atheroma documented by non-invasive vascular imaging or catheter angiography 6. any aortic aneurysm documented by non-invasive vascular imaging or catheter angiography that is considered atherosclerotic
• Negative pregnancy test in a female who has had any menses in the last 18 months and has not had surgery that would make her unable to become pregnant
• Subject is willing and able to return for all follow-up evaluations required by the protocol
• Subject is available by phone
• Subject understands the purpose and requirements of the study and can make him/herself understood
• Subject has provided informed consent (use of a LAR is not permitted)
• Previous treatment of target lesion with a stent, angioplasty, or other mechanical device, including mechanical thrombectomy for the qualifying stroke, or plan to perform one of these procedures
• Plan to perform concomitant endarterectomy, angioplasty or stenting of an extracranial vessel tandem to the symptomatic intracranial stenosis
• Intracranial tumor (except meningioma) or any intracranial vascular malformation
• Thrombolytic therapy within 24 hours prior to randomization
• Progressive neurological signs within 24 hours prior to randomization
• History of any intracranial hemorrhage (parenchymal, subarachnoid, subdural, epidural)
• Intracranial arterial stenosis due to: arterial dissection; MoyaMoya disease; any known vasculitic disease; herpes zoster, varicella zoster or other viral vasculopathy; neurosyphilis; any other intracranial infection; any intracranial stenosis associated with CSF pleocytosis; radiation induced vasculopathy; fibromuscular dysplasia; sickle cell disease; neurofibromatosis; benign angiopathy of central nervous system; postpartum angiopathy; suspected vasospastic process; reversible cerebral vasoconstriction syndrome (RCVS); suspected recanalized embolus
• Presence of any of the following unequivocal cardiac sources of embolism: chronic or paroxysmal atrial fibrillation, mitral stenosis, mechanical valve, endocarditis, intracardiac clot or vegetation, myocardial infarction within three months, left atrial spontaneous echo contrast
• Known allergy or contraindication to aspirin, rivaroxaban, clopidogrel, or ticagrelor
• Uncontrolled severe hypertension (systolic pressure > 180 mm Hg or diastolic pressure > 115 mm Hg), active peptic ulcer disease, major systemic hemorrhage within 30 days prior to randomization, active bleed or bleeding diathesis, platelets < 100,000, hematocrit < 30, INR > 1.5, clotting factor abnormality that increases the risk of bleeding, current alcohol or substance abuse, severe liver impairment (AST or ALT > 3 x normal, cirrhosis), or CrCl < 15 mL/min or on dialysis
• Major surgery (including stenting of any vessel; open femoral, aortic, or carotid surgery; or cardiac surgery) within previous 30 days prior to randomization or planned in the next 90 days after randomization
• Any condition other than intracranial arterial stenosis that requires the subject to take any antithrombotic medication other than aspirin (NOTE: exceptions allowed for subcutaneous heparin for deep vein thrombosis (DVT) prophylaxis)
• Dementia or psychiatric problem that prevents the subject from following an outpatient program reliably
• Co-morbid conditions that may limit survival to less than 12 months
• Pregnancy or of childbearing potential and unwilling to use contraception for the duration of this study, or currently breastfeeding
• Current or anticipated concomitant oral or intravenous therapy with strong CYP3A4 inhibitors or CYP3A4 substrates that cannot be stopped for the course of this study
• Enrollment in another study that would conflict with the current study